{"id":542467,"date":"2021-09-28T10:35:35","date_gmt":"2021-09-28T10:35:35","guid":{"rendered":"https:\/\/www.indcareer.com\/schools\/?p=542467"},"modified":"2022-12-26T09:40:30","modified_gmt":"2022-12-26T09:40:30","slug":"rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals","status":"publish","type":"post","link":"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/","title":{"rendered":"RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals"},"content":{"rendered":"\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">Class 12: Maths Chapter 19 solutions. Complete Class 12 Maths Chapter 19 Notes.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\">RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals<\/h2>\n\n\n\n<p><meta http-equiv=\"content-type\" content=\"text\/html; charset=utf-8\">RD Sharma 12th Maths Chapter 19, Class 12 Maths Chapter 19 solutions<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.1 Page No: 19.4<\/h4>\n\n\n\n<p><strong>1. Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"84\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-1.gif\" alt=\"\" class=\"wp-image-542471\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"184\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-2.png\" alt=\"\" class=\"wp-image-542472\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-2.png 323w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-2-300x171.png 300w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"103\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-3.gif\" alt=\"\" class=\"wp-image-542473\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-thumbnail\"><img loading=\"lazy\" decoding=\"async\" width=\"150\" height=\"150\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-4-150x150.png\" alt=\"\" class=\"wp-image-542474\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-4-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-4-400x397.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-4-200x200.png 200w\" sizes=\"auto, (max-width: 150px) 100vw, 150px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"97\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-5.gif\" alt=\"\" class=\"wp-image-542475\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"417\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-6.png\" alt=\"\" class=\"wp-image-542476\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-6.png 258w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-6-186x300.png 186w\" sizes=\"auto, (max-width: 258px) 100vw, 258px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"99\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-7.gif\" alt=\"\" class=\"wp-image-542477\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"469\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-8.png\" alt=\"\" class=\"wp-image-542478\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-8.png 370w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-8-237x300.png 237w\" sizes=\"auto, (max-width: 370px) 100vw, 370px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"281\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-9.png\" alt=\"\" class=\"wp-image-542479\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"89\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-10.gif\" alt=\"\" class=\"wp-image-542480\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"258\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-11.png\" alt=\"\" class=\"wp-image-542481\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-11.png 606w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-11-300x128.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-11-400x170.png 400w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"106\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-12.gif\" alt=\"\" class=\"wp-image-542482\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"365\" height=\"424\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-13.png\" alt=\"\" class=\"wp-image-542483\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-13.png 365w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-13-258x300.png 258w\" sizes=\"auto, (max-width: 365px) 100vw, 365px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"132\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-14.gif\" alt=\"\" class=\"wp-image-542484\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p>Solution:<\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"369\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-15.png\" alt=\"\" class=\"wp-image-542485\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-15.png 370w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-15-300x300.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-15-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-15-200x200.png 200w\" sizes=\"auto, (max-width: 370px) 100vw, 370px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"363\" height=\"94\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-16.png\" alt=\"\" class=\"wp-image-542486\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-16.png 363w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-16-300x78.png 300w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"134\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-17.gif\" alt=\"\" class=\"wp-image-542487\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"234\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-18.png\" alt=\"\" class=\"wp-image-542488\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>2. Evaluate:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"177\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-19.gif\" alt=\"\" class=\"wp-image-542489\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"410\" height=\"378\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-20.png\" alt=\"\" class=\"wp-image-542490\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-20.png 410w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-20-300x277.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-20-400x369.png 400w\" sizes=\"auto, (max-width: 410px) 100vw, 410px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"146\" height=\"144\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-21.png\" alt=\"\" class=\"wp-image-542491\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"182\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-22.gif\" alt=\"\" class=\"wp-image-542492\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-23.png\" alt=\"\" class=\"wp-image-542493\" width=\"269\" height=\"213\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-23.png 648w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-23-300x237.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-23-400x316.png 400w\" sizes=\"auto, (max-width: 269px) 100vw, 269px\" \/><\/figure>\n\n\n\n<p><strong>3. Evaluate:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"215\" height=\"63\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-24.png\" alt=\"\" class=\"wp-image-542494\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"260\" height=\"526\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-25.png\" alt=\"\" class=\"wp-image-542495\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-25.png 260w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-25-148x300.png 148w\" sizes=\"auto, (max-width: 260px) 100vw, 260px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.2 Page No: 19.14<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals (1 \u2013 44):<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-26.png\" alt=\"\" class=\"wp-image-542496\" width=\"221\" height=\"46\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-26.png 355w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-26-300x63.png 300w\" sizes=\"auto, (max-width: 221px) 100vw, 221px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-27.png\" alt=\"\" class=\"wp-image-542497\" width=\"267\" height=\"598\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-27.png 374w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-27-134x300.png 134w\" sizes=\"auto, (max-width: 267px) 100vw, 267px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-28.gif\" alt=\"\" class=\"wp-image-542498\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"334\" height=\"626\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-29.png\" alt=\"\" class=\"wp-image-542499\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-29.png 334w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-29-160x300.png 160w\" sizes=\"auto, (max-width: 334px) 100vw, 334px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"149\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-30.png\" alt=\"\" class=\"wp-image-542500\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"226\" height=\"53\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-30-1.png\" alt=\"\" class=\"wp-image-542501\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"252\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-31.gif\" alt=\"\" class=\"wp-image-542502\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"604\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-32.png\" alt=\"\" class=\"wp-image-542503\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-32.png 370w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-32-184x300.png 184w\" sizes=\"auto, (max-width: 370px) 100vw, 370px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-33.gif\" alt=\"\" class=\"wp-image-542504\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given,<\/p>\n\n\n\n<p>\u222b(2 \u2013 3x)(3 + 2x)(1 \u2013 2x) dx<\/p>\n\n\n\n<p>= \u222b(6 + 4x \u2013 9x \u2013 6x<sup>2<\/sup>)(1 \u2013 2x) dx<\/p>\n\n\n\n<p>= \u222b(6 \u2013 5x \u2013 6x<sup>2<\/sup>)(1 \u2013 2x) dx<\/p>\n\n\n\n<p>= \u222b(6 \u2013 5x \u2013 6x<sup>2<\/sup>&nbsp;\u2013 12x + 10x<sup>2<\/sup>&nbsp;+ 12x<sup>3<\/sup>) dx<\/p>\n\n\n\n<p>= \u222b(6 \u2013 17x + 4x<sup>2<\/sup>&nbsp;+ 12x<sup>3<\/sup>) dx<\/p>\n\n\n\n<p>Upon splitting the above, we have<\/p>\n\n\n\n<p>= \u222b6 dx \u2013 \u222b17x dx + \u222b4x<sup>2<\/sup>&nbsp;dx + \u222b12x<sup>3<\/sup>&nbsp;dx<\/p>\n\n\n\n<p>On integrating using formula,<\/p>\n\n\n\n<p>\u222bx<sup>n<\/sup>&nbsp;dx = x<sup>n+1<\/sup>\/n+1<\/p>\n\n\n\n<p>we get<\/p>\n\n\n\n<p>= 6x \u2013 17\/(1+1) x<sup>1+1<\/sup>&nbsp;+ 4\/(2+1) x<sup>2+1<\/sup>&nbsp;+ 12\/(3+1) x<sup>3+1<\/sup>&nbsp;+ c<\/p>\n\n\n\n<p>= 6x \u2013 17x<sup>2<\/sup>\/2 + 4x<sup>3<\/sup>\/3 + 3x<sup>4<\/sup>&nbsp;+ c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"329\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-35.gif\" alt=\"\" class=\"wp-image-542505\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"392\" height=\"174\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-36.png\" alt=\"\" class=\"wp-image-542506\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-36.png 392w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-36-300x133.png 300w\" sizes=\"auto, (max-width: 392px) 100vw, 392px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"399\" height=\"552\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-37.png\" alt=\"\" class=\"wp-image-542507\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-37.png 399w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-37-217x300.png 217w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"195\" height=\"49\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-38.gif\" alt=\"\" class=\"wp-image-542508\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"330\" height=\"177\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-39.png\" alt=\"\" class=\"wp-image-542509\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-39.png 330w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-39-300x161.png 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"479\" height=\"295\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-40.png\" alt=\"\" class=\"wp-image-542510\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-40.png 479w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-40-300x185.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-40-400x246.png 400w\" sizes=\"auto, (max-width: 479px) 100vw, 479px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"143\" height=\"48\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-41.gif\" alt=\"\" class=\"wp-image-542511\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"518\" height=\"403\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-42.png\" alt=\"\" class=\"wp-image-542512\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-42.png 518w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-42-300x233.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-42-400x311.png 400w\" sizes=\"auto, (max-width: 518px) 100vw, 518px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"322\" height=\"331\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-43.png\" alt=\"\" class=\"wp-image-542513\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-43.png 322w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-43-292x300.png 292w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"261\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-44.gif\" alt=\"\" class=\"wp-image-542514\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"313\" height=\"335\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-45.png\" alt=\"\" class=\"wp-image-542515\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-45.png 313w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-45-280x300.png 280w\" sizes=\"auto, (max-width: 313px) 100vw, 313px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-46.png\" alt=\"\" class=\"wp-image-542516\" width=\"238\" height=\"208\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-46.png 397w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-46-300x262.png 300w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-47.gif\" alt=\"\" class=\"wp-image-542517\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"652\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-48.png\" alt=\"\" class=\"wp-image-542518\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-48.png 309w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-48-142x300.png 142w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"241\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-49.png\" alt=\"\" class=\"wp-image-542519\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"202\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-50.gif\" alt=\"\" class=\"wp-image-542520\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"483\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-51.png\" alt=\"\" class=\"wp-image-542521\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-51.png 344w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-51-214x300.png 214w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"250\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-52.png\" alt=\"\" class=\"wp-image-542522\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-53.gif\" alt=\"\" class=\"wp-image-542523\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"521\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-54.png\" alt=\"\" class=\"wp-image-542524\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-54.png 326w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-54-188x300.png 188w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"417\" height=\"382\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-55.png\" alt=\"\" class=\"wp-image-542525\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-55.png 417w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-55-300x275.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-55-400x366.png 400w\" sizes=\"auto, (max-width: 417px) 100vw, 417px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"48\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-56.gif\" alt=\"\" class=\"wp-image-542526\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"330\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-57.png\" alt=\"\" class=\"wp-image-542527\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-57.png 357w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-57-300x277.png 300w\" sizes=\"auto, (max-width: 357px) 100vw, 357px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"424\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-58.png\" alt=\"\" class=\"wp-image-542528\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-58.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-58-197x300.png 197w\" sizes=\"auto, (max-width: 279px) 100vw, 279px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-59.gif\" alt=\"\" class=\"wp-image-542529\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"296\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-60.png\" alt=\"\" class=\"wp-image-542530\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-60.png 384w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-60-300x231.png 300w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"310\" height=\"380\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-61.png\" alt=\"\" class=\"wp-image-542531\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-61.png 310w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-61-245x300.png 245w\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"209\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-62.gif\" alt=\"\" class=\"wp-image-542532\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"364\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-63.png\" alt=\"\" class=\"wp-image-542533\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-63.png 344w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-63-284x300.png 284w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"340\" height=\"505\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-64.png\" alt=\"\" class=\"wp-image-542534\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-64.png 340w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-64-202x300.png 202w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"194\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-65.gif\" alt=\"\" class=\"wp-image-542535\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"325\" height=\"282\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-66.png\" alt=\"\" class=\"wp-image-542536\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-66.png 325w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-66-300x260.png 300w\" sizes=\"auto, (max-width: 325px) 100vw, 325px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"358\" height=\"540\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-67.png\" alt=\"\" class=\"wp-image-542537\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-67.png 358w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-67-199x300.png 199w\" sizes=\"auto, (max-width: 358px) 100vw, 358px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"233\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-68.gif\" alt=\"\" class=\"wp-image-542538\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"509\" height=\"188\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-69.png\" alt=\"\" class=\"wp-image-542539\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-69.png 509w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-69-300x111.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-69-400x148.png 400w\" sizes=\"auto, (max-width: 509px) 100vw, 509px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-70.png\" alt=\"\" class=\"wp-image-542540\" width=\"462\" height=\"373\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-70.png 777w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-70-300x242.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-70-768x620.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-70-400x323.png 400w\" sizes=\"auto, (max-width: 462px) 100vw, 462px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.3 Page No: 19.23<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-71.gif\" alt=\"\" class=\"wp-image-542541\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"433\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-72.png\" alt=\"\" class=\"wp-image-542542\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-72.png 369w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-72-256x300.png 256w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"258\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-73.gif\" alt=\"\" class=\"wp-image-542543\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"309\" height=\"132\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-74.png\" alt=\"\" class=\"wp-image-542544\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-74.png 309w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-74-300x128.png 300w\" sizes=\"auto, (max-width: 309px) 100vw, 309px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"188\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-75.png\" alt=\"\" class=\"wp-image-542545\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-75.png 319w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-75-300x177.png 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"235\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-76.gif\" alt=\"\" class=\"wp-image-542546\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-77.png\" alt=\"\" class=\"wp-image-542547\" width=\"279\" height=\"273\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-77.png 440w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-77-300x293.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-77-400x391.png 400w\" sizes=\"auto, (max-width: 279px) 100vw, 279px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"138\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-78.gif\" alt=\"\" class=\"wp-image-542548\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"310\" height=\"498\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-79.png\" alt=\"\" class=\"wp-image-542549\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-79.png 310w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-79-187x300.png 187w\" sizes=\"auto, (max-width: 310px) 100vw, 310px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"376\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-80.png\" alt=\"\" class=\"wp-image-542550\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-80.png 301w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-80-240x300.png 240w\" sizes=\"auto, (max-width: 301px) 100vw, 301px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"184\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-81.gif\" alt=\"\" class=\"wp-image-542551\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"305\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-82.png\" alt=\"\" class=\"wp-image-542552\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-82.png 326w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-82-300x281.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"236\" height=\"206\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-83.png\" alt=\"\" class=\"wp-image-542553\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-84.gif\" alt=\"\" class=\"wp-image-542554\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"323\" height=\"602\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-85.png\" alt=\"\" class=\"wp-image-542555\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-85.png 323w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-85-161x300.png 161w\" sizes=\"auto, (max-width: 323px) 100vw, 323px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-86.png\" alt=\"\" class=\"wp-image-542558\" width=\"302\" height=\"123\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-86.png 469w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-86-300x122.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-86-400x163.png 400w\" sizes=\"auto, (max-width: 302px) 100vw, 302px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"148\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-87-1.gif\" alt=\"\" class=\"wp-image-542557\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"428\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-88.png\" alt=\"\" class=\"wp-image-542559\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-88.png 343w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-88-240x300.png 240w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"219\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-89.gif\" alt=\"\" class=\"wp-image-542560\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"136\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-90.png\" alt=\"\" class=\"wp-image-542561\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"390\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-91.png\" alt=\"\" class=\"wp-image-542562\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-91.png 328w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-91-252x300.png 252w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/c-users-tnluser-downloads-codecogseqn-2020-01-28t110337-898-gif.gif\" alt=\"\" class=\"wp-image-542563\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"296\" height=\"403\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-93.png\" alt=\"\" class=\"wp-image-542564\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-93.png 296w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-93-220x300.png 220w\" sizes=\"auto, (max-width: 296px) 100vw, 296px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"194\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-94.png\" alt=\"\" class=\"wp-image-542565\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.4 Page No: 19.30<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-95.gif\" alt=\"\" class=\"wp-image-542566\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"492\" height=\"609\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-96.png\" alt=\"\" class=\"wp-image-542567\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-96.png 492w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-96-242x300.png 242w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-96-400x495.png 400w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"116\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-97.gif\" alt=\"\" class=\"wp-image-542568\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"554\" height=\"613\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-98.png\" alt=\"\" class=\"wp-image-542569\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-98.png 554w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-98-271x300.png 271w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-98-400x443.png 400w\" sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"156\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-99.gif\" alt=\"\" class=\"wp-image-542570\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"134\" height=\"86\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-100.png\" alt=\"\" class=\"wp-image-542571\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"518\" height=\"555\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101.png\" alt=\"\" class=\"wp-image-542572\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101.png 518w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101-280x300.png 280w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101-400x429.png 400w\" sizes=\"auto, (max-width: 518px) 100vw, 518px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101a.png\" alt=\"\" class=\"wp-image-542573\" width=\"449\" height=\"221\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101a.png 811w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101a-300x148.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101a-768x379.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-101a-400x197.png 400w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.5 Page No: 19.33<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"141\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-102.gif\" alt=\"\" class=\"wp-image-542574\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"568\" height=\"611\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-103.png\" alt=\"\" class=\"wp-image-542575\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-103.png 568w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-103-279x300.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-103-400x430.png 400w\" sizes=\"auto, (max-width: 568px) 100vw, 568px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"51\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-104.png\" alt=\"\" class=\"wp-image-542576\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"139\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-105.gif\" alt=\"\" class=\"wp-image-542577\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"577\" height=\"396\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-106.png\" alt=\"\" class=\"wp-image-542578\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-106.png 577w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-106-300x206.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-106-400x275.png 400w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"132\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-107.gif\" alt=\"\" class=\"wp-image-542579\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"569\" height=\"394\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-108.png\" alt=\"\" class=\"wp-image-542580\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-108.png 569w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-108-300x208.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-108-400x277.png 400w\" sizes=\"auto, (max-width: 569px) 100vw, 569px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"287\" height=\"386\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-109.png\" alt=\"\" class=\"wp-image-542581\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-109.png 287w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-109-223x300.png 223w\" sizes=\"auto, (max-width: 287px) 100vw, 287px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-110.gif\" alt=\"\" class=\"wp-image-542582\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"479\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111.png\" alt=\"\" class=\"wp-image-542583\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111.png 366w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111-229x300.png 229w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111a.png\" alt=\"\" class=\"wp-image-542584\" width=\"294\" height=\"152\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111a.png 544w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111a-300x155.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-111a-400x207.png 400w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"389\" height=\"558\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-112.png\" alt=\"\" class=\"wp-image-542585\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-112.png 389w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-112-209x300.png 209w\" sizes=\"auto, (max-width: 389px) 100vw, 389px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"142\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-113.gif\" alt=\"\" class=\"wp-image-542586\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"447\" height=\"288\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-114.png\" alt=\"\" class=\"wp-image-542587\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-114.png 447w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-114-300x193.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-114-400x258.png 400w\" sizes=\"auto, (max-width: 447px) 100vw, 447px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"616\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-115.png\" alt=\"\" class=\"wp-image-542588\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-115.png 342w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-115-167x300.png 167w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"282\" height=\"122\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-116.png\" alt=\"\" class=\"wp-image-542589\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.6 Page No: 19.36<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-117.gif\" alt=\"\" class=\"wp-image-542590\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"279\" height=\"382\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-118.png\" alt=\"\" class=\"wp-image-542591\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-118.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-118-219x300.png 219w\" sizes=\"auto, (max-width: 279px) 100vw, 279px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-119.gif\" alt=\"\" class=\"wp-image-542592\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"290\" height=\"184\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-120.png\" alt=\"\" class=\"wp-image-542593\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"450\" height=\"300\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-121.png\" alt=\"\" class=\"wp-image-542594\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-121.png 450w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-121-300x200.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-121-400x267.png 400w\" sizes=\"auto, (max-width: 450px) 100vw, 450px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"124\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-122.gif\" alt=\"\" class=\"wp-image-542595\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"529\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-123.png\" alt=\"\" class=\"wp-image-542596\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-123.png 373w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-123-212x300.png 212w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"366\" height=\"195\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-124.png\" alt=\"\" class=\"wp-image-542597\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-124.png 366w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-124-300x160.png 300w\" sizes=\"auto, (max-width: 366px) 100vw, 366px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"119\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-125.gif\" alt=\"\" class=\"wp-image-542598\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-126.png\" alt=\"\" class=\"wp-image-542599\" width=\"247\" height=\"343\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-126.png 406w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-126-216x300.png 216w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-126-400x556.png 400w\" sizes=\"auto, (max-width: 247px) 100vw, 247px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.7 Page No: 19.38<\/h4>\n\n\n\n<p><strong>Integrate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-127.gif\" alt=\"\" class=\"wp-image-542600\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"449\" height=\"554\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-128.png\" alt=\"\" class=\"wp-image-542601\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-128.png 449w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-128-243x300.png 243w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-128-400x494.png 400w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-129.gif\" alt=\"\" class=\"wp-image-542602\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"409\" height=\"494\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-130.png\" alt=\"\" class=\"wp-image-542603\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-130.png 409w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-130-248x300.png 248w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-130-400x483.png 400w\" sizes=\"auto, (max-width: 409px) 100vw, 409px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"238\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-131.gif\" alt=\"\" class=\"wp-image-542604\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"203\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-132.png\" alt=\"\" class=\"wp-image-542605\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-132.png 362w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-132-300x168.png 300w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"444\" height=\"389\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-133.png\" alt=\"\" class=\"wp-image-542606\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-133.png 444w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-133-300x263.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-133-400x350.png 400w\" sizes=\"auto, (max-width: 444px) 100vw, 444px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.8 Page No: 19.47<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"181\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-134.gif\" alt=\"\" class=\"wp-image-542607\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"411\" height=\"547\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135.png\" alt=\"\" class=\"wp-image-542608\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135.png 411w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135-225x300.png 225w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135-300x400.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-135-400x532.png 400w\" sizes=\"auto, (max-width: 411px) 100vw, 411px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-136.png\" alt=\"\" class=\"wp-image-542609\" width=\"170\" height=\"47\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-136.png\" alt=\"\" class=\"wp-image-542609\" width=\"170\" height=\"47\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"488\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137.png\" alt=\"\" class=\"wp-image-542610\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137.png 463w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137-285x300.png 285w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-137-400x422.png 400w\" sizes=\"auto, (max-width: 463px) 100vw, 463px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-138.png\" alt=\"\" class=\"wp-image-542611\" width=\"146\" height=\"38\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Given,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-139a.png\" alt=\"\" class=\"wp-image-542612\" width=\"118\" height=\"46\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"462\" height=\"248\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-139.png\" alt=\"\" class=\"wp-image-542613\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-139.png 462w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-139-300x161.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-139-400x215.png 400w\" sizes=\"auto, (max-width: 462px) 100vw, 462px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"185\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-140.png\" alt=\"\" class=\"wp-image-542614\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"127\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-141.gif\" alt=\"\" class=\"wp-image-542615\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"355\" height=\"637\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-142.png\" alt=\"\" class=\"wp-image-542616\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-142.png 355w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-142-167x300.png 167w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"271\" height=\"110\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-143.png\" alt=\"\" class=\"wp-image-542617\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-144.png\" alt=\"\" class=\"wp-image-542618\" width=\"204\" height=\"47\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-144.png 321w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-144-300x69.png 300w\" sizes=\"auto, (max-width: 204px) 100vw, 204px\" \/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"289\" height=\"630\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-145.png\" alt=\"\" class=\"wp-image-542619\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-145.png 289w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-145-138x300.png 138w\" sizes=\"auto, (max-width: 289px) 100vw, 289px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"137\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-146.gif\" alt=\"\" class=\"wp-image-542620\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"584\" height=\"565\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-147.png\" alt=\"\" class=\"wp-image-542621\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-147.png 584w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-147-300x290.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-147-400x387.png 400w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/figure>\n\n\n\n<p>Therefore,<\/p>\n\n\n\n<p>= cos (b \u2013 a)x + sin(b \u2013 a) log |sin(x \u2013 b)| + c, where c is an arbitrary constant.<\/p>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.9 Page No: 19.57<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<p><strong>&nbsp;dx<\/strong><\/p>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"363\" height=\"323\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-149.png\" alt=\"\" class=\"wp-image-542622\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-149.png 363w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-149-300x267.png 300w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"49\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-150.gif\" alt=\"\" class=\"wp-image-542623\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"204\" height=\"252\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-151.png\" alt=\"\" class=\"wp-image-542624\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-152.png\" alt=\"\" class=\"wp-image-542625\" width=\"322\" height=\"303\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-152.png 592w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-152-300x282.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-152-400x376.png 400w\" sizes=\"auto, (max-width: 322px) 100vw, 322px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"48\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-153.gif\" alt=\"\" class=\"wp-image-542626\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"398\" height=\"335\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-154.png\" alt=\"\" class=\"wp-image-542627\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-154.png 398w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-154-300x253.png 300w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"131\" height=\"82\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-155-1.png\" alt=\"\" class=\"wp-image-542628\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"163\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-156.gif\" alt=\"\" class=\"wp-image-542629\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"376\" height=\"370\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-157.png\" alt=\"\" class=\"wp-image-542630\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-157.png 376w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-157-300x295.png 300w\" sizes=\"auto, (max-width: 376px) 100vw, 376px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"184\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-158.gif\" alt=\"\" class=\"wp-image-542631\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"407\" height=\"234\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-159.png\" alt=\"\" class=\"wp-image-542632\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-159.png 407w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-159-300x172.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-159-400x230.png 400w\" sizes=\"auto, (max-width: 407px) 100vw, 407px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-160.png\" alt=\"\" class=\"wp-image-542633\" width=\"360\" height=\"247\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-160.png 591w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-160-300x206.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-160-400x275.png 400w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"154\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-161.gif\" alt=\"\" class=\"wp-image-542634\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"357\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-162.png\" alt=\"\" class=\"wp-image-542635\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-162.png 369w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-162-300x290.png 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-163.gif\" alt=\"\" class=\"wp-image-542636\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-164.png\" alt=\"\" class=\"wp-image-542637\" width=\"296\" height=\"342\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-164.png 588w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-164-260x300.png 260w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-164-400x462.png 400w\" sizes=\"auto, (max-width: 296px) 100vw, 296px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"62\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-165.gif\" alt=\"\" class=\"wp-image-542638\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"399\" height=\"370\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-166.png\" alt=\"\" class=\"wp-image-542639\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-166.png 399w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-166-300x278.png 300w\" sizes=\"auto, (max-width: 399px) 100vw, 399px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"148\" height=\"127\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-167.png\" alt=\"\" class=\"wp-image-542640\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"173\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-168.gif\" alt=\"\" class=\"wp-image-542641\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"336\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-169.png\" alt=\"\" class=\"wp-image-542642\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-169.png 368w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-169-300x274.png 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-170.gif\" alt=\"\" class=\"wp-image-542643\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"404\" height=\"153\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-171.png\" alt=\"\" class=\"wp-image-542644\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-171.png 404w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-171-300x114.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-171-400x151.png 400w\" sizes=\"auto, (max-width: 404px) 100vw, 404px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-172.png\" alt=\"\" class=\"wp-image-542646\" width=\"290\" height=\"223\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-172.png 484w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-172-300x231.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-172-400x308.png 400w\" sizes=\"auto, (max-width: 290px) 100vw, 290px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.10 Page No: 19.65<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"156\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-173.gif\" alt=\"\" class=\"wp-image-542647\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"419\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-174.png\" alt=\"\" class=\"wp-image-542648\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-174.png 589w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-174-300x213.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-174-400x285.png 400w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"140\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-175.gif\" alt=\"\" class=\"wp-image-542649\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"276\" height=\"221\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-176.png\" alt=\"\" class=\"wp-image-542650\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"513\" height=\"647\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-177.png\" alt=\"\" class=\"wp-image-542651\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-177.png 513w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-177-238x300.png 238w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-177-400x504.png 400w\" sizes=\"auto, (max-width: 513px) 100vw, 513px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-178.png\" alt=\"\" class=\"wp-image-542652\" width=\"371\" height=\"153\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-178.png 699w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-178-300x124.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-178-400x165.png 400w\" sizes=\"auto, (max-width: 371px) 100vw, 371px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"151\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-179.gif\" alt=\"\" class=\"wp-image-542653\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"500\" height=\"584\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-180.png\" alt=\"\" class=\"wp-image-542654\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-180.png 500w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-180-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-180-400x467.png 400w\" sizes=\"auto, (max-width: 500px) 100vw, 500px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"534\" height=\"97\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-181.png\" alt=\"\" class=\"wp-image-542655\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-181.png 534w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-181-300x54.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-181-400x73.png 400w\" sizes=\"auto, (max-width: 534px) 100vw, 534px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-182.png\" alt=\"\" class=\"wp-image-542656\" width=\"158\" height=\"49\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"429\" height=\"533\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183.png\" alt=\"\" class=\"wp-image-542657\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183.png 429w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183-241x300.png 241w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183-400x497.png 400w\" sizes=\"auto, (max-width: 429px) 100vw, 429px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183a.png\" alt=\"\" class=\"wp-image-542658\" width=\"386\" height=\"176\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183a.png 625w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183a-300x137.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-183a-400x182.png 400w\" sizes=\"auto, (max-width: 386px) 100vw, 386px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-184.gif\" alt=\"\" class=\"wp-image-542659\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"165\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-185.png\" alt=\"\" class=\"wp-image-542660\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-185.png 412w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-185-300x120.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-185-400x160.png 400w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-186.png\" alt=\"\" class=\"wp-image-542661\" width=\"489\" height=\"356\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-186.png 879w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-186-300x219.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-186-768x560.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-186-400x292.png 400w\" sizes=\"auto, (max-width: 489px) 100vw, 489px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.11 Page No: 19.69<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-187.gif\" alt=\"\" class=\"wp-image-542663\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"458\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-188.png\" alt=\"\" class=\"wp-image-542664\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-188.png 346w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-188-227x300.png 227w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-188-150x200.png 150w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-189.gif\" alt=\"\" class=\"wp-image-542665\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"138\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-190.png\" alt=\"\" class=\"wp-image-542666\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"405\" height=\"538\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191.png\" alt=\"\" class=\"wp-image-542667\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191.png 405w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191-226x300.png 226w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191-300x400.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-191-400x531.png 400w\" sizes=\"auto, (max-width: 405px) 100vw, 405px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-192.gif\" alt=\"\" class=\"wp-image-542668\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"314\" height=\"232\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-193.png\" alt=\"\" class=\"wp-image-542669\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-193.png 314w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-193-300x222.png 300w\" sizes=\"auto, (max-width: 314px) 100vw, 314px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"420\" height=\"536\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-194.png\" alt=\"\" class=\"wp-image-542670\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-194.png 420w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-194-235x300.png 235w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-194-400x510.png 400w\" sizes=\"auto, (max-width: 420px) 100vw, 420px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"170\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-195.gif\" alt=\"\" class=\"wp-image-542671\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"333\" height=\"179\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-196.png\" alt=\"\" class=\"wp-image-542672\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-196.png 333w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-196-300x161.png 300w\" sizes=\"auto, (max-width: 333px) 100vw, 333px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"385\" height=\"296\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-197.png\" alt=\"\" class=\"wp-image-542673\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-197.png 385w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-197-300x231.png 300w\" sizes=\"auto, (max-width: 385px) 100vw, 385px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"124\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-198.gif\" alt=\"\" class=\"wp-image-542674\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"457\" height=\"624\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-199.png\" alt=\"\" class=\"wp-image-542675\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-199.png 457w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-199-220x300.png 220w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-199-400x546.png 400w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"303\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-200.png\" alt=\"\" class=\"wp-image-542676\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-200.png 455w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-200-300x200.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-200-400x266.png 400w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-201.gif\" alt=\"\" class=\"wp-image-542677\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"305\" height=\"543\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-202.png\" alt=\"\" class=\"wp-image-542678\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-202.png 305w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-202-169x300.png 169w\" sizes=\"auto, (max-width: 305px) 100vw, 305px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"233\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-203.png\" alt=\"\" class=\"wp-image-542679\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-203.png 446w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-203-300x157.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-203-400x209.png 400w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.12 Page No: 19.73<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"174\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-204.gif\" alt=\"\" class=\"wp-image-542680\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"505\" height=\"639\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-205.png\" alt=\"\" class=\"wp-image-542681\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-205.png 505w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-205-237x300.png 237w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-205-400x506.png 400w\" sizes=\"auto, (max-width: 505px) 100vw, 505px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"120\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-206.gif\" alt=\"\" class=\"wp-image-542682\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"577\" height=\"604\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-207.png\" alt=\"\" class=\"wp-image-542683\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-207.png 577w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-207-287x300.png 287w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-207-400x419.png 400w\" sizes=\"auto, (max-width: 577px) 100vw, 577px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"558\" height=\"236\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-208.png\" alt=\"\" class=\"wp-image-542684\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-208.png 558w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-208-300x127.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-208-400x169.png 400w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"557\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-209.png\" alt=\"\" class=\"wp-image-542685\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-209.png 557w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-209-300x23.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-209-400x30.png 400w\" sizes=\"auto, (max-width: 557px) 100vw, 557px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"123\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-210.gif\" alt=\"\" class=\"wp-image-542687\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"585\" height=\"647\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-211.png\" alt=\"\" class=\"wp-image-542688\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-211.png 585w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-211-271x300.png 271w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-211-400x442.png 400w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"128\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-212.png\" alt=\"\" class=\"wp-image-542689\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-213.gif\" alt=\"\" class=\"wp-image-542690\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"313\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-214.png\" alt=\"\" class=\"wp-image-542691\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-214.png 368w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-214-300x255.png 300w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"174\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-215.gif\" alt=\"\" class=\"wp-image-542692\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"219\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-216.png\" alt=\"\" class=\"wp-image-542693\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-217.png\" alt=\"\" class=\"wp-image-542694\" width=\"189\" height=\"232\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-217.png 296w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-217-245x300.png 245w\" sizes=\"auto, (max-width: 189px) 100vw, 189px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.13 Page No: 19.79<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"49\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-218.gif\" alt=\"\" class=\"wp-image-542695\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"484\" height=\"565\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219.png\" alt=\"\" class=\"wp-image-542696\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219.png 484w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219-400x467.png 400w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219a.png\" alt=\"\" class=\"wp-image-542697\" width=\"185\" height=\"146\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219a.png 325w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-219a-300x236.png 300w\" sizes=\"auto, (max-width: 185px) 100vw, 185px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-220.gif\" alt=\"\" class=\"wp-image-542698\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"627\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-221.png\" alt=\"\" class=\"wp-image-542699\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-221.png 278w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-221-133x300.png 133w\" sizes=\"auto, (max-width: 278px) 100vw, 278px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"255\" height=\"270\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-222.png\" alt=\"\" class=\"wp-image-542700\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"117\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-223.png\" alt=\"\" class=\"wp-image-542701\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-223.png 338w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-223-300x104.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.14 Page No: 19.83<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-224.gif\" alt=\"\" class=\"wp-image-542702\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-225.png\" alt=\"\" class=\"wp-image-542703\" width=\"406\" height=\"353\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-225.png 669w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-225-300x261.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-225-400x347.png 400w\" sizes=\"auto, (max-width: 406px) 100vw, 406px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-226.gif\" alt=\"\" class=\"wp-image-542704\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"456\" height=\"335\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227.png\" alt=\"\" class=\"wp-image-542705\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227.png 456w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227-300x220.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227-400x294.png 400w\" sizes=\"auto, (max-width: 456px) 100vw, 456px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"367\" height=\"86\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227a-1.png\" alt=\"\" class=\"wp-image-542706\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227a-1.png 367w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-227a-1-300x70.png 300w\" sizes=\"auto, (max-width: 367px) 100vw, 367px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"326\" height=\"195\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-228.png\" alt=\"\" class=\"wp-image-542707\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-228.png 326w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-228-300x179.png 300w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-229.gif\" alt=\"\" class=\"wp-image-542708\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-230.png\" alt=\"\" class=\"wp-image-542709\" width=\"361\" height=\"259\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-230.png 664w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-230-300x215.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-230-400x287.png 400w\" sizes=\"auto, (max-width: 361px) 100vw, 361px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"131\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-231.gif\" alt=\"\" class=\"wp-image-542710\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"483\" height=\"447\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-232.png\" alt=\"\" class=\"wp-image-542711\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-232.png 483w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-232-300x278.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-232-400x370.png 400w\" sizes=\"auto, (max-width: 483px) 100vw, 483px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-233.png\" alt=\"\" class=\"wp-image-542712\" width=\"326\" height=\"302\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-233.png 562w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-233-300x278.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-233-400x370.png 400w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"158\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-234.gif\" alt=\"\" class=\"wp-image-542713\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-235-1.png\" alt=\"\" class=\"wp-image-542715\" width=\"336\" height=\"332\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-235-1.png 601w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-235-1-300x297.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-235-1-400x395.png 400w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.15 Page No: 19.86<\/h4>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"198\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-237.gif\" alt=\"\" class=\"wp-image-542716\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"388\" height=\"616\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-238.png\" alt=\"\" class=\"wp-image-542717\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-238.png 388w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-238-189x300.png 189w\" sizes=\"auto, (max-width: 388px) 100vw, 388px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"110\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-239.png\" alt=\"\" class=\"wp-image-542718\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-239.png 354w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-239-300x93.png 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-240-1.png\" alt=\"\" class=\"wp-image-542719\" width=\"321\" height=\"168\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-240-1.png 519w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-240-1-300x157.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-240-1-400x209.png 400w\" sizes=\"auto, (max-width: 321px) 100vw, 321px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-241.gif\" alt=\"\" class=\"wp-image-542720\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"352\" height=\"601\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242.png\" alt=\"\" class=\"wp-image-542721\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242.png 352w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242-176x300.png 176w\" sizes=\"auto, (max-width: 352px) 100vw, 352px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242a.png\" alt=\"\" class=\"wp-image-542722\" width=\"252\" height=\"343\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242a.png 453w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242a-221x300.png 221w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-242a-400x544.png 400w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"312\" height=\"158\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-243.png\" alt=\"\" class=\"wp-image-542723\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-243.png 312w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-243-300x152.png 300w\" sizes=\"auto, (max-width: 312px) 100vw, 312px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-244.gif\" alt=\"\" class=\"wp-image-542724\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"380\" height=\"643\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-245.png\" alt=\"\" class=\"wp-image-542725\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-245.png 380w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-245-177x300.png 177w\" sizes=\"auto, (max-width: 380px) 100vw, 380px\" \/><\/figure>\n\n\n\n<p>By using,<br><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"369\" height=\"63\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246a.png\" alt=\"\" class=\"wp-image-542726\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246a.png 369w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246a-300x51.png 300w\" sizes=\"auto, (max-width: 369px) 100vw, 369px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"347\" height=\"189\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246.png\" alt=\"\" class=\"wp-image-542727\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246.png 347w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-246-300x163.png 300w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-247.gif\" alt=\"\" class=\"wp-image-542728\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"469\" height=\"633\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-248.png\" alt=\"\" class=\"wp-image-542729\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-248.png 469w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-248-222x300.png 222w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-248-400x540.png 400w\" sizes=\"auto, (max-width: 469px) 100vw, 469px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-249.png\" alt=\"\" class=\"wp-image-542730\" width=\"355\" height=\"271\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-249.png 515w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-249-300x229.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-249-400x305.png 400w\" sizes=\"auto, (max-width: 355px) 100vw, 355px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-250.png\" alt=\"\" class=\"wp-image-542731\" width=\"182\" height=\"48\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"416\" height=\"475\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-251.png\" alt=\"\" class=\"wp-image-542732\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-251.png 416w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-251-263x300.png 263w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-251-400x457.png 400w\" sizes=\"auto, (max-width: 416px) 100vw, 416px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.16 Page No: 19.90<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-252.png\" alt=\"\" class=\"wp-image-542733\" width=\"143\" height=\"47\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"540\" height=\"328\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-253.png\" alt=\"\" class=\"wp-image-542734\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-253.png 540w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-253-300x182.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-253-400x243.png 400w\" sizes=\"auto, (max-width: 540px) 100vw, 540px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"137\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-254.gif\" alt=\"\" class=\"wp-image-542735\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"355\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-255.png\" alt=\"\" class=\"wp-image-542736\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-255.png 418w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-255-300x255.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-255-400x340.png 400w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"278\" height=\"130\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-256.png\" alt=\"\" class=\"wp-image-542737\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"240\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-257.gif\" alt=\"\" class=\"wp-image-542738\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"616\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-258.png\" alt=\"\" class=\"wp-image-542739\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-258.png 412w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-258-201x300.png 201w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-258-400x598.png 400w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-259.gif\" alt=\"\" class=\"wp-image-542740\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"301\" height=\"621\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-260.png\" alt=\"\" class=\"wp-image-542741\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-260.png 301w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-260-145x300.png 145w\" sizes=\"auto, (max-width: 301px) 100vw, 301px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-261.png\" alt=\"\" class=\"wp-image-542742\" width=\"347\" height=\"326\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-261.png 520w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-261-300x282.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-261-400x375.png 400w\" sizes=\"auto, (max-width: 347px) 100vw, 347px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-262.png\" alt=\"\" class=\"wp-image-542743\" width=\"241\" height=\"164\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-262.png 367w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-262-300x204.png 300w\" sizes=\"auto, (max-width: 241px) 100vw, 241px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"147\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-263.gif\" alt=\"\" class=\"wp-image-542744\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"596\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-264.png\" alt=\"\" class=\"wp-image-542745\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-264.png 354w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-264-178x300.png 178w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-265.png\" alt=\"\" class=\"wp-image-542747\" width=\"270\" height=\"92\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-265.png 436w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-265-300x102.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-265-400x136.png 400w\" sizes=\"auto, (max-width: 270px) 100vw, 270px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.17 Page No: 19.93<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"160\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-266.gif\" alt=\"\" class=\"wp-image-542746\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"476\" height=\"631\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-267.png\" alt=\"\" class=\"wp-image-542748\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-267.png 476w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-267-226x300.png 226w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-267-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-267-400x530.png 400w\" sizes=\"auto, (max-width: 476px) 100vw, 476px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-268.gif\" alt=\"\" class=\"wp-image-542749\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"592\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-269.png\" alt=\"\" class=\"wp-image-542750\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-269.png 598w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-269-300x297.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-269-400x396.png 400w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"150\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-270.png\" alt=\"\" class=\"wp-image-542751\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"172\" height=\"150\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-271.png\" alt=\"\" class=\"wp-image-542752\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/c-users-tnluser-downloads-codecogseqn-2020-01-30t120903-568-gif.gif\" alt=\"\" class=\"wp-image-542753\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"471\" height=\"632\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-273.png\" alt=\"\" class=\"wp-image-542754\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-273.png 471w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-273-224x300.png 224w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-273-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-273-400x537.png 400w\" sizes=\"auto, (max-width: 471px) 100vw, 471px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"294\" height=\"331\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-274.png\" alt=\"\" class=\"wp-image-542755\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-274.png 294w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-274-266x300.png 266w\" sizes=\"auto, (max-width: 294px) 100vw, 294px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"206\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/c-users-tnluser-downloads-codecogseqn-2020-01-30t121259-367-gif.gif\" alt=\"\" class=\"wp-image-542756\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"590\" height=\"422\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-276.png\" alt=\"\" class=\"wp-image-542757\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-276.png 590w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-276-300x215.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-276-400x286.png 400w\" sizes=\"auto, (max-width: 590px) 100vw, 590px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277.png\" alt=\"\" class=\"wp-image-542758\" width=\"403\" height=\"366\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277.png 905w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277-300x271.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277-768x695.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277-900x819.png 900w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-277-400x362.png 400w\" sizes=\"auto, (max-width: 403px) 100vw, 403px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.18 Page No: 19.98<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-278.gif\" alt=\"\" class=\"wp-image-542759\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-280.png\" alt=\"\" class=\"wp-image-542760\" width=\"362\" height=\"350\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-280.png 686w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-280-300x291.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-280-400x388.png 400w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-282.png\" alt=\"\" class=\"wp-image-542761\" width=\"176\" height=\"51\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-283.png\" alt=\"\" class=\"wp-image-542762\" width=\"328\" height=\"233\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-283.png 561w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-283-300x213.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-283-400x284.png 400w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-284.gif\" alt=\"\" class=\"wp-image-542763\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"346\" height=\"277\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-285.png\" alt=\"\" class=\"wp-image-542764\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-285.png 346w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-285-300x240.png 300w\" sizes=\"auto, (max-width: 346px) 100vw, 346px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-286.gif\" alt=\"\" class=\"wp-image-542765\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>Let sin x = t<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"495\" height=\"312\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-287.png\" alt=\"\" class=\"wp-image-542766\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-287.png 495w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-287-300x189.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-287-400x252.png 400w\" sizes=\"auto, (max-width: 495px) 100vw, 495px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-288.gif\" alt=\"\" class=\"wp-image-542767\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"432\" height=\"468\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-289.png\" alt=\"\" class=\"wp-image-542768\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-289.png 432w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-289-277x300.png 277w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-289-400x433.png 400w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"149\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-290.gif\" alt=\"\" class=\"wp-image-542769\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-291.png\" alt=\"\" class=\"wp-image-542770\" width=\"389\" height=\"307\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-291.png 676w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-291-300x237.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-291-400x315.png 400w\" sizes=\"auto, (max-width: 389px) 100vw, 389px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"217\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-292.gif\" alt=\"\" class=\"wp-image-542771\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"344\" height=\"402\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-293.png\" alt=\"\" class=\"wp-image-542772\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-293.png 344w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-293-257x300.png 257w\" sizes=\"auto, (max-width: 344px) 100vw, 344px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"330\" height=\"127\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-294.png\" alt=\"\" class=\"wp-image-542773\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-294.png 330w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-294-300x115.png 300w\" sizes=\"auto, (max-width: 330px) 100vw, 330px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-295.gif\" alt=\"\" class=\"wp-image-542774\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-296.png\" alt=\"\" class=\"wp-image-542775\" width=\"432\" height=\"369\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-296.png 668w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-296-300x256.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-296-400x341.png 400w\" sizes=\"auto, (max-width: 432px) 100vw, 432px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-298.png\" alt=\"\" class=\"wp-image-542776\" width=\"146\" height=\"147\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-298.png 287w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-298-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-298-200x200.png 200w\" sizes=\"auto, (max-width: 146px) 100vw, 146px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"528\" height=\"228\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-299.png\" alt=\"\" class=\"wp-image-542777\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-299.png 528w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-299-300x130.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-299-400x173.png 400w\" sizes=\"auto, (max-width: 528px) 100vw, 528px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.19 Page No: 19.104<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"178\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-300.gif\" alt=\"\" class=\"wp-image-542778\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"620\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-301.png\" alt=\"\" class=\"wp-image-542779\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-301.png 604w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-301-292x300.png 292w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-301-400x411.png 400w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/figure>\n\n\n\n<p>We will solve I<sub>1<\/sub>&nbsp;and I<sub>2<\/sub>&nbsp;individually.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"593\" height=\"638\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-302-1.png\" alt=\"\" class=\"wp-image-542781\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-302-1.png 593w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-302-1-279x300.png 279w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-302-1-400x430.png 400w\" sizes=\"auto, (max-width: 593px) 100vw, 593px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"340\" height=\"233\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-303.png\" alt=\"\" class=\"wp-image-542782\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-303.png 340w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-303-300x206.png 300w\" sizes=\"auto, (max-width: 340px) 100vw, 340px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-304.png\" alt=\"\" class=\"wp-image-542783\" width=\"324\" height=\"273\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-304.png 652w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-304-300x253.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-304-400x337.png 400w\" sizes=\"auto, (max-width: 324px) 100vw, 324px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-305.gif\" alt=\"\" class=\"wp-image-542784\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-306.png\" alt=\"\" class=\"wp-image-542785\" width=\"558\" height=\"330\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-306.png 896w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-306-300x178.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-306-768x456.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-306-400x238.png 400w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"320\" height=\"603\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-307.png\" alt=\"\" class=\"wp-image-542786\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-307.png 320w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-307-159x300.png 159w\" sizes=\"auto, (max-width: 320px) 100vw, 320px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"218\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-308.png\" alt=\"\" class=\"wp-image-542787\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-308.png 595w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-308-300x110.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-308-400x147.png 400w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"578\" height=\"640\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309.png\" alt=\"\" class=\"wp-image-542788\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309.png 578w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309-271x300.png 271w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309-400x443.png 400w\" sizes=\"auto, (max-width: 578px) 100vw, 578px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309a.png\" alt=\"\" class=\"wp-image-542789\" width=\"336\" height=\"74\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309a.png 510w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309a-300x66.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-309a-400x88.png 400w\" sizes=\"auto, (max-width: 336px) 100vw, 336px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-310.gif\" alt=\"\" class=\"wp-image-542790\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"608\" height=\"124\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-311.png\" alt=\"\" class=\"wp-image-542791\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-311.png 608w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-311-300x61.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-311-400x82.png 400w\" sizes=\"auto, (max-width: 608px) 100vw, 608px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"631\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-312.png\" alt=\"\" class=\"wp-image-542792\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-312.png 609w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-312-290x300.png 290w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-312-400x414.png 400w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"584\" height=\"198\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-313.png\" alt=\"\" class=\"wp-image-542793\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-313.png 584w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-313-300x102.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-313-400x136.png 400w\" sizes=\"auto, (max-width: 584px) 100vw, 584px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"636\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-314.png\" alt=\"\" class=\"wp-image-542794\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-314.png 594w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-314-280x300.png 280w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-314-400x428.png 400w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"331\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-315.png\" alt=\"\" class=\"wp-image-542795\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-315.png 331w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-315-300x43.png 300w\" sizes=\"auto, (max-width: 331px) 100vw, 331px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"189\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-316.gif\" alt=\"\" class=\"wp-image-542796\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"148\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-317.png\" alt=\"\" class=\"wp-image-542797\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"612\" height=\"613\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318.png\" alt=\"\" class=\"wp-image-542798\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318.png 612w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318-300x300.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318-400x401.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-318-200x200.png 200w\" sizes=\"auto, (max-width: 612px) 100vw, 612px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"586\" height=\"248\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-319.png\" alt=\"\" class=\"wp-image-542799\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-319.png 586w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-319-300x127.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-319-400x169.png 400w\" sizes=\"auto, (max-width: 586px) 100vw, 586px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"599\" height=\"605\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-320.png\" alt=\"\" class=\"wp-image-542800\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-320.png 599w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-320-297x300.png 297w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-320-400x404.png 400w\" sizes=\"auto, (max-width: 599px) 100vw, 599px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"338\" height=\"94\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-321.png\" alt=\"\" class=\"wp-image-542801\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-321.png 338w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-321-300x83.png 300w\" sizes=\"auto, (max-width: 338px) 100vw, 338px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-322.gif\" alt=\"\" class=\"wp-image-542802\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"611\" height=\"635\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-323.png\" alt=\"\" class=\"wp-image-542803\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-323.png 611w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-323-289x300.png 289w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-323-400x416.png 400w\" sizes=\"auto, (max-width: 611px) 100vw, 611px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"319\" height=\"253\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-324.png\" alt=\"\" class=\"wp-image-542804\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-324.png 319w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-324-300x238.png 300w\" sizes=\"auto, (max-width: 319px) 100vw, 319px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"597\" height=\"599\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325.png\" alt=\"\" class=\"wp-image-542805\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325.png 597w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325-300x300.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325-400x401.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-325-200x200.png 200w\" sizes=\"auto, (max-width: 597px) 100vw, 597px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"501\" height=\"270\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-326.png\" alt=\"\" class=\"wp-image-542806\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-326.png 501w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-326-300x162.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-326-400x216.png 400w\" sizes=\"auto, (max-width: 501px) 100vw, 501px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"357\" height=\"49\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-327.png\" alt=\"\" class=\"wp-image-542807\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-327.png 357w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-327-300x41.png 300w\" sizes=\"auto, (max-width: 357px) 100vw, 357px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.20 Page No: 19.106<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-328.gif\" alt=\"\" class=\"wp-image-542808\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"496\" height=\"644\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-329.png\" alt=\"\" class=\"wp-image-542809\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-329.png 496w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-329-231x300.png 231w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-329-400x519.png 400w\" sizes=\"auto, (max-width: 496px) 100vw, 496px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"480\" height=\"629\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-330.png\" alt=\"\" class=\"wp-image-542810\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-330.png 480w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-330-229x300.png 229w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-330-400x524.png 400w\" sizes=\"auto, (max-width: 480px) 100vw, 480px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"454\" height=\"145\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-331.png\" alt=\"\" class=\"wp-image-542811\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-331.png 454w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-331-300x96.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-331-400x128.png 400w\" sizes=\"auto, (max-width: 454px) 100vw, 454px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"168\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-332.gif\" alt=\"\" class=\"wp-image-542812\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"494\" height=\"619\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-333.png\" alt=\"\" class=\"wp-image-542813\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-333.png 494w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-333-239x300.png 239w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-333-400x501.png 400w\" sizes=\"auto, (max-width: 494px) 100vw, 494px\" \/><\/figure>\n\n\n\n<p>\u21d2&nbsp;1 = (A + B) x + (3A \u2013 2B)<\/p>\n\n\n\n<p>\u21d2&nbsp;Then A + B = 0 \u2026 (1)<\/p>\n\n\n\n<p>And 3A \u2013 2B = 1 \u2026 (2)<\/p>\n\n\n\n<p>Solving (1) and (2),<\/p>\n\n\n\n<p>2 \u00d7 (1)&nbsp;\u2192&nbsp;2A + 2B = 0<\/p>\n\n\n\n<p>1 \u00d7 (2)&nbsp;\u2192&nbsp;3A \u2013 2B = 1<\/p>\n\n\n\n<p>5A = 1<\/p>\n\n\n\n<p>\u2234&nbsp;A = 1\/5<\/p>\n\n\n\n<p>Substituting A value in (1),<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"641\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-334.png\" alt=\"\" class=\"wp-image-542814\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-334.png 604w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-334-283x300.png 283w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-334-400x425.png 400w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"118\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-335-1.png\" alt=\"\" class=\"wp-image-542815\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-335-1.png 412w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-335-1-300x86.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-335-1-400x115.png 400w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/figure>\n\n\n\n<p>Or I = log|(x \u2013 2)\/(x + 3)| + x + c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-336.gif\" alt=\"\" class=\"wp-image-542816\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"492\" height=\"644\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-337.png\" alt=\"\" class=\"wp-image-542817\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-337.png 492w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-337-229x300.png 229w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-337-400x524.png 400w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"223\" height=\"111\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-338.png\" alt=\"\" class=\"wp-image-542818\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"402\" height=\"652\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-339-1.png\" alt=\"\" class=\"wp-image-542819\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-339-1.png 402w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-339-1-185x300.png 185w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-339-1-400x649.png 400w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"428\" height=\"219\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-340.png\" alt=\"\" class=\"wp-image-542820\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-340.png 428w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-340-300x154.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-340-400x205.png 400w\" sizes=\"auto, (max-width: 428px) 100vw, 428px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"179\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-341.gif\" alt=\"\" class=\"wp-image-542821\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"368\" height=\"623\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-342.png\" alt=\"\" class=\"wp-image-542822\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-342.png 368w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-342-177x300.png 177w\" sizes=\"auto, (max-width: 368px) 100vw, 368px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"231\" height=\"164\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-343.png\" alt=\"\" class=\"wp-image-542823\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"363\" height=\"649\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-344.png\" alt=\"\" class=\"wp-image-542824\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-344.png 363w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-344-168x300.png 168w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"532\" height=\"178\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-345.png\" alt=\"\" class=\"wp-image-542825\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-345.png 532w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-345-300x100.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-345-400x134.png 400w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"552\" height=\"546\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-346.png\" alt=\"\" class=\"wp-image-542826\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-346.png 552w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-346-300x297.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-346-400x396.png 400w\" sizes=\"auto, (max-width: 552px) 100vw, 552px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-347.gif\" alt=\"\" class=\"wp-image-542827\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"521\" height=\"641\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-348.png\" alt=\"\" class=\"wp-image-542828\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-348.png 521w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-348-244x300.png 244w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-348-400x492.png 400w\" sizes=\"auto, (max-width: 521px) 100vw, 521px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"523\" height=\"636\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-349.png\" alt=\"\" class=\"wp-image-542829\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-349.png 523w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-349-247x300.png 247w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-349-400x486.png 400w\" sizes=\"auto, (max-width: 523px) 100vw, 523px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"343\" height=\"217\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-350.png\" alt=\"\" class=\"wp-image-542830\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-350.png 343w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-350-300x190.png 300w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"412\" height=\"620\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-351.png\" alt=\"\" class=\"wp-image-542831\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-351.png 412w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-351-199x300.png 199w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-351-400x602.png 400w\" sizes=\"auto, (max-width: 412px) 100vw, 412px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"266\" height=\"193\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-352.png\" alt=\"\" class=\"wp-image-542832\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"589\" height=\"649\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-353.png\" alt=\"\" class=\"wp-image-542833\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-353.png 589w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-353-272x300.png 272w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-353-400x441.png 400w\" sizes=\"auto, (max-width: 589px) 100vw, 589px\" \/><\/figure>\n\n\n\n<p>Hence,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"434\" height=\"62\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-354.png\" alt=\"\" class=\"wp-image-542834\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-354.png 434w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-354-300x43.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-354-400x57.png 400w\" sizes=\"auto, (max-width: 434px) 100vw, 434px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.21 Page No: 19.110<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-355.gif\" alt=\"\" class=\"wp-image-542835\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"630\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-356.png\" alt=\"\" class=\"wp-image-542836\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-356.png 511w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-356-243x300.png 243w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-356-400x493.png 400w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"564\" height=\"644\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-357.png\" alt=\"\" class=\"wp-image-542837\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-357.png 564w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-357-263x300.png 263w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-357-400x457.png 400w\" sizes=\"auto, (max-width: 564px) 100vw, 564px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"508\" height=\"56\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-358.png\" alt=\"\" class=\"wp-image-542838\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-358.png 508w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-358-300x33.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-358-400x44.png 400w\" sizes=\"auto, (max-width: 508px) 100vw, 508px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-359.gif\" alt=\"\" class=\"wp-image-542839\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"478\" height=\"632\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-360.png\" alt=\"\" class=\"wp-image-542840\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-360.png 478w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-360-227x300.png 227w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-360-400x529.png 400w\" sizes=\"auto, (max-width: 478px) 100vw, 478px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"342\" height=\"262\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-361.png\" alt=\"\" class=\"wp-image-542841\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-361.png 342w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-361-300x230.png 300w\" sizes=\"auto, (max-width: 342px) 100vw, 342px\" \/><\/figure>\n\n\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-363.gif\" alt=\"\" class=\"wp-image-542842\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"538\" height=\"629\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-364.png\" alt=\"\" class=\"wp-image-542843\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-364.png 538w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-364-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-364-400x468.png 400w\" sizes=\"auto, (max-width: 538px) 100vw, 538px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"535\" height=\"625\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365.png\" alt=\"\" class=\"wp-image-542844\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365.png 535w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365-400x467.png 400w\" sizes=\"auto, (max-width: 535px) 100vw, 535px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365a.png\" alt=\"\" class=\"wp-image-542845\" width=\"396\" height=\"321\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365a.png 789w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365a-300x244.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365a-768x624.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-365a-400x325.png 400w\" sizes=\"auto, (max-width: 396px) 100vw, 396px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"379\" height=\"184\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-366.png\" alt=\"\" class=\"wp-image-542846\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-366.png 379w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-366-300x146.png 300w\" sizes=\"auto, (max-width: 379px) 100vw, 379px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"556\" height=\"473\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-367.png\" alt=\"\" class=\"wp-image-542847\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-367.png 556w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-367-300x255.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-367-400x340.png 400w\" sizes=\"auto, (max-width: 556px) 100vw, 556px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-368.gif\" alt=\"\" class=\"wp-image-542848\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"435\" height=\"579\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1.png\" alt=\"\" class=\"wp-image-542849\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1.png 435w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1-225x300.png 225w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1-300x400.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-369-1-400x532.png 400w\" sizes=\"auto, (max-width: 435px) 100vw, 435px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"381\" height=\"316\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-370.png\" alt=\"\" class=\"wp-image-542850\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-370.png 381w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-370-300x249.png 300w\" sizes=\"auto, (max-width: 381px) 100vw, 381px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"196\" height=\"44\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-371.gif\" alt=\"\" class=\"wp-image-542851\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"528\" height=\"632\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-372.png\" alt=\"\" class=\"wp-image-542852\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-372.png 528w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-372-251x300.png 251w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-372-400x479.png 400w\" sizes=\"auto, (max-width: 528px) 100vw, 528px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"389\" height=\"605\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-373.png\" alt=\"\" class=\"wp-image-542853\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-373.png 389w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-373-193x300.png 193w\" sizes=\"auto, (max-width: 389px) 100vw, 389px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"560\" height=\"318\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-374.png\" alt=\"\" class=\"wp-image-542854\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-374.png 560w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-374-300x170.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-374-400x227.png 400w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"560\" height=\"175\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-375.png\" alt=\"\" class=\"wp-image-542855\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-375.png 560w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-375-300x94.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-375-400x125.png 400w\" sizes=\"auto, (max-width: 560px) 100vw, 560px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.22 Page No: 19.114<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-376.gif\" alt=\"\" class=\"wp-image-542856\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"601\" height=\"574\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-377.png\" alt=\"\" class=\"wp-image-542857\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-377.png 601w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-377-300x287.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-377-400x382.png 400w\" sizes=\"auto, (max-width: 601px) 100vw, 601px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"227\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-378.gif\" alt=\"\" class=\"wp-image-542858\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"578\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-379.png\" alt=\"\" class=\"wp-image-542859\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-379.png 594w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-379-300x292.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-379-400x389.png 400w\" sizes=\"auto, (max-width: 594px) 100vw, 594px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"162\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-380.gif\" alt=\"\" class=\"wp-image-542860\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"351\" height=\"141\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-381.png\" alt=\"\" class=\"wp-image-542861\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-381.png 351w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-381-300x121.png 300w\" sizes=\"auto, (max-width: 351px) 100vw, 351px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"397\" height=\"619\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-382.png\" alt=\"\" class=\"wp-image-542862\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-382.png 397w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-382-192x300.png 192w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"354\" height=\"112\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-383.png\" alt=\"\" class=\"wp-image-542863\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-383.png 354w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-383-300x95.png 300w\" sizes=\"auto, (max-width: 354px) 100vw, 354px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-384.gif\" alt=\"\" class=\"wp-image-542864\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"643\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-385.png\" alt=\"\" class=\"wp-image-542865\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-385.png 362w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-385-169x300.png 169w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-386.png\" alt=\"\" class=\"wp-image-542866\" width=\"331\" height=\"242\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-386.png 535w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-386-300x220.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-386-400x293.png 400w\" sizes=\"auto, (max-width: 331px) 100vw, 331px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.23 Page No: 19.117<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-387.gif\" alt=\"\" class=\"wp-image-542867\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"435\" height=\"600\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-388.png\" alt=\"\" class=\"wp-image-542868\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-388.png 435w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-388-218x300.png 218w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-388-400x552.png 400w\" sizes=\"auto, (max-width: 435px) 100vw, 435px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"297\" height=\"50\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-389.png\" alt=\"\" class=\"wp-image-542869\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-390.png\" alt=\"\" class=\"wp-image-542870\" width=\"204\" height=\"42\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-390.png 330w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-390-300x62.png 300w\" sizes=\"auto, (max-width: 204px) 100vw, 204px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"165\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-391.gif\" alt=\"\" class=\"wp-image-542871\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"634\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-392.png\" alt=\"\" class=\"wp-image-542872\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-392.png 491w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-392-232x300.png 232w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-392-400x516.png 400w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-393.png\" alt=\"\" class=\"wp-image-542873\" width=\"348\" height=\"159\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-393.png 608w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-393-300x137.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-393-400x182.png 400w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"166\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-394.gif\" alt=\"\" class=\"wp-image-542874\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"484\" height=\"614\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-395.png\" alt=\"\" class=\"wp-image-542875\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-395.png 484w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-395-236x300.png 236w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-395-400x507.png 400w\" sizes=\"auto, (max-width: 484px) 100vw, 484px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-396.png\" alt=\"\" class=\"wp-image-542876\" width=\"403\" height=\"280\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-396.png 706w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-396-300x208.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-396-400x278.png 400w\" sizes=\"auto, (max-width: 403px) 100vw, 403px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"168\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-397.gif\" alt=\"\" class=\"wp-image-542877\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"491\" height=\"620\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-398.png\" alt=\"\" class=\"wp-image-542878\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-398.png 491w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-398-238x300.png 238w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-398-400x505.png 400w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-399.png\" alt=\"\" class=\"wp-image-542879\" width=\"363\" height=\"440\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-399.png 597w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-399-247x300.png 247w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-399-400x486.png 400w\" sizes=\"auto, (max-width: 363px) 100vw, 363px\" \/><\/figure>\n\n\n\n<p>5.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"201\" height=\"56\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-400.png\" alt=\"\" class=\"wp-image-542880\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"575\" height=\"385\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-401.png\" alt=\"\" class=\"wp-image-542881\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-401.png 575w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-401-300x201.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-401-400x268.png 400w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"567\" height=\"460\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-402-1.png\" alt=\"\" class=\"wp-image-542882\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-402-1.png 567w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-402-1-300x243.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-402-1-400x325.png 400w\" sizes=\"auto, (max-width: 567px) 100vw, 567px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.24 Page No: 19.122<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"153\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-403.gif\" alt=\"\" class=\"wp-image-542883\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"634\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-404.png\" alt=\"\" class=\"wp-image-542884\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-404.png 602w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-404-285x300.png 285w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-404-400x421.png 400w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"401\" height=\"623\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-405.png\" alt=\"\" class=\"wp-image-542885\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-405.png 401w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-405-193x300.png 193w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-405-400x621.png 400w\" sizes=\"auto, (max-width: 401px) 100vw, 401px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"285\" height=\"92\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-406.png\" alt=\"\" class=\"wp-image-542886\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"155\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-407.gif\" alt=\"\" class=\"wp-image-542887\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"629\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-408.png\" alt=\"\" class=\"wp-image-542888\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-408.png 606w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-408-289x300.png 289w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-408-400x415.png 400w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"403\" height=\"273\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-409.png\" alt=\"\" class=\"wp-image-542889\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-409.png 403w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-409-300x203.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-409-400x271.png 400w\" sizes=\"auto, (max-width: 403px) 100vw, 403px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"395\" height=\"545\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-410.png\" alt=\"\" class=\"wp-image-542890\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-410.png 395w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-410-217x300.png 217w\" sizes=\"auto, (max-width: 395px) 100vw, 395px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"247\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-411.gif\" alt=\"\" class=\"wp-image-542891\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"217\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-412.png\" alt=\"\" class=\"wp-image-542892\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-412.png 602w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-412-300x108.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-412-600x217.png 600w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-412-400x144.png 400w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"627\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-413.png\" alt=\"\" class=\"wp-image-542893\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-413.png 603w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-413-289x300.png 289w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-413-400x416.png 400w\" sizes=\"auto, (max-width: 603px) 100vw, 603px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"448\" height=\"274\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-414.png\" alt=\"\" class=\"wp-image-542894\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-414.png 448w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-414-300x183.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-414-400x245.png 400w\" sizes=\"auto, (max-width: 448px) 100vw, 448px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"464\" height=\"621\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-415.png\" alt=\"\" class=\"wp-image-542895\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-415.png 464w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-415-224x300.png 224w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-415-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-415-400x535.png 400w\" sizes=\"auto, (max-width: 464px) 100vw, 464px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"612\" height=\"253\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-416.png\" alt=\"\" class=\"wp-image-542896\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-416.png 612w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-416-300x124.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-416-400x165.png 400w\" sizes=\"auto, (max-width: 612px) 100vw, 612px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"373\" height=\"448\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-417-1.png\" alt=\"\" class=\"wp-image-542897\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-417-1.png 373w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-417-1-250x300.png 250w\" sizes=\"auto, (max-width: 373px) 100vw, 373px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"171\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-418.gif\" alt=\"\" class=\"wp-image-542898\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"248\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419.png\" alt=\"\" class=\"wp-image-542899\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419.png 602w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419-300x124.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419-600x248.png 600w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419-400x165.png 400w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419a.png\" alt=\"\" class=\"wp-image-542900\" width=\"491\" height=\"311\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419a.png 905w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419a-300x190.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419a-768x487.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-419a-400x254.png 400w\" sizes=\"auto, (max-width: 491px) 100vw, 491px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-420.png\" alt=\"\" class=\"wp-image-542901\" width=\"453\" height=\"389\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-420.png 764w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-420-300x258.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-420-400x343.png 400w\" sizes=\"auto, (max-width: 453px) 100vw, 453px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"418\" height=\"340\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-422.png\" alt=\"\" class=\"wp-image-542902\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-422.png 418w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-422-300x244.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-422-400x325.png 400w\" sizes=\"auto, (max-width: 418px) 100vw, 418px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"233\" height=\"42\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-423.gif\" alt=\"\" class=\"wp-image-542903\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"487\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-424.png\" alt=\"\" class=\"wp-image-542904\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-424.png 604w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-424-300x242.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-424-400x323.png 400w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"504\" height=\"637\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-425.png\" alt=\"\" class=\"wp-image-542905\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-425.png 504w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-425-237x300.png 237w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-425-400x506.png 400w\" sizes=\"auto, (max-width: 504px) 100vw, 504px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"288\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-426.png\" alt=\"\" class=\"wp-image-542907\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-426.png 384w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-426-300x225.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-426-200x150.png 200w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"328\" height=\"154\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-427.png\" alt=\"\" class=\"wp-image-542908\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-427.png 328w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-427-300x141.png 300w\" sizes=\"auto, (max-width: 328px) 100vw, 328px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.25 Page No: 19.133<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"129\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-428.gif\" alt=\"\" class=\"wp-image-542909\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-429.png\" alt=\"\" class=\"wp-image-542910\" width=\"438\" height=\"284\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-429.png 719w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-429-300x194.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-429-400x259.png 400w\" sizes=\"auto, (max-width: 438px) 100vw, 438px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"161\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-430.gif\" alt=\"\" class=\"wp-image-542911\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"360\" height=\"477\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-431.png\" alt=\"\" class=\"wp-image-542912\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-431.png 360w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-431-226x300.png 226w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-431-150x200.png 150w\" sizes=\"auto, (max-width: 360px) 100vw, 360px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-432.png\" alt=\"\" class=\"wp-image-542914\" width=\"252\" height=\"181\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-432.png 407w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-432-300x216.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-432-400x288.png 400w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"137\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-433.gif\" alt=\"\" class=\"wp-image-542913\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-434.png\" alt=\"\" class=\"wp-image-542915\" width=\"244\" height=\"334\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-434.png 458w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-434-219x300.png 219w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-434-400x547.png 400w\" sizes=\"auto, (max-width: 244px) 100vw, 244px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"103\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-435.gif\" alt=\"\" class=\"wp-image-542916\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-436-1.png\" alt=\"\" class=\"wp-image-542917\" width=\"278\" height=\"239\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-436-1.png 463w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-436-1-300x258.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-436-1-400x344.png 400w\" sizes=\"auto, (max-width: 278px) 100vw, 278px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"109\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-437-1.gif\" alt=\"\" class=\"wp-image-542919\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-438.png\" alt=\"\" class=\"wp-image-542918\" width=\"252\" height=\"282\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-438.png 476w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-438-268x300.png 268w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-438-400x448.png 400w\" sizes=\"auto, (max-width: 252px) 100vw, 252px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.26 Page No: 19.143<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"215\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-439.gif\" alt=\"\" class=\"wp-image-542920\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-440.png\" alt=\"\" class=\"wp-image-542921\" width=\"308\" height=\"261\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-440.png 547w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-440-300x254.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-440-400x339.png 400w\" sizes=\"auto, (max-width: 308px) 100vw, 308px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"197\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-441.gif\" alt=\"\" class=\"wp-image-542922\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"371\" height=\"409\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-442.png\" alt=\"\" class=\"wp-image-542923\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-442.png 371w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-442-272x300.png 272w\" sizes=\"auto, (max-width: 371px) 100vw, 371px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"299\" height=\"175\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-443.png\" alt=\"\" class=\"wp-image-542924\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"207\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-444.gif\" alt=\"\" class=\"wp-image-542925\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-445.png\" alt=\"\" class=\"wp-image-542926\" width=\"398\" height=\"458\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-445.png 658w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-445-260x300.png 260w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-445-400x461.png 400w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"277\" height=\"396\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-446.png\" alt=\"\" class=\"wp-image-542927\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-446.png 277w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-446-210x300.png 210w\" sizes=\"auto, (max-width: 277px) 100vw, 277px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"245\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-447.gif\" alt=\"\" class=\"wp-image-542928\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"398\" height=\"269\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-448.png\" alt=\"\" class=\"wp-image-542929\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-448.png 398w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-448-300x203.png 300w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"175\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-449.gif\" alt=\"\" class=\"wp-image-542930\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"358\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-450.png\" alt=\"\" class=\"wp-image-542931\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-450.png 298w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-450-250x300.png 250w\" sizes=\"auto, (max-width: 298px) 100vw, 298px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.27 Page No: 19.149<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"154\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-451.gif\" alt=\"\" class=\"wp-image-542932\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-452.png\" alt=\"\" class=\"wp-image-542933\" width=\"329\" height=\"436\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-452.png 584w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-452-226x300.png 226w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-452-150x200.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-452-400x530.png 400w\" sizes=\"auto, (max-width: 329px) 100vw, 329px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"199\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-453.gif\" alt=\"\" class=\"wp-image-542934\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454.png\" alt=\"\" class=\"wp-image-542935\" width=\"343\" height=\"342\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454.png 640w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454-300x300.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454-400x399.png 400w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-454-200x200.png 200w\" sizes=\"auto, (max-width: 343px) 100vw, 343px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"157\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-455.gif\" alt=\"\" class=\"wp-image-542936\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-456.png\" alt=\"\" class=\"wp-image-542937\" width=\"440\" height=\"256\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-456.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-456-300x174.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-456-400x232.png 400w\" sizes=\"auto, (max-width: 440px) 100vw, 440px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"398\" height=\"195\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-457.png\" alt=\"\" class=\"wp-image-542938\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-457.png 398w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-457-300x147.png 300w\" sizes=\"auto, (max-width: 398px) 100vw, 398px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-458.gif\" alt=\"\" class=\"wp-image-542939\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-459.png\" alt=\"\" class=\"wp-image-542940\" width=\"473\" height=\"366\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-459.png 777w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-459-300x232.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-459-768x594.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-459-400x309.png 400w\" sizes=\"auto, (max-width: 473px) 100vw, 473px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"188\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-460.gif\" alt=\"\" class=\"wp-image-542941\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"421\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-461.png\" alt=\"\" class=\"wp-image-542942\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-461.png 374w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-461-267x300.png 267w\" sizes=\"auto, (max-width: 374px) 100vw, 374px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.28 Page No: 19.154<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-462.gif\" alt=\"\" class=\"wp-image-542944\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"492\" height=\"423\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-463.png\" alt=\"\" class=\"wp-image-542945\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-463.png 492w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-463-300x258.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-463-400x344.png 400w\" sizes=\"auto, (max-width: 492px) 100vw, 492px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"182\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-464.gif\" alt=\"\" class=\"wp-image-542946\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"335\" height=\"170\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-465.png\" alt=\"\" class=\"wp-image-542947\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-465.png 335w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-465-300x152.png 300w\" sizes=\"auto, (max-width: 335px) 100vw, 335px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"575\" height=\"383\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-466.png\" alt=\"\" class=\"wp-image-542948\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-466.png 575w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-466-300x200.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-466-400x266.png 400w\" sizes=\"auto, (max-width: 575px) 100vw, 575px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"148\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-467.gif\" alt=\"\" class=\"wp-image-542949\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"558\" height=\"409\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-468.png\" alt=\"\" class=\"wp-image-542950\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-468.png 558w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-468-300x220.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-468-400x293.png 400w\" sizes=\"auto, (max-width: 558px) 100vw, 558px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"359\" height=\"36\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-469.png\" alt=\"\" class=\"wp-image-542951\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-469.png 359w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-469-300x30.png 300w\" sizes=\"auto, (max-width: 359px) 100vw, 359px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"194\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-470.gif\" alt=\"\" class=\"wp-image-542952\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"595\" height=\"473\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-471.png\" alt=\"\" class=\"wp-image-542953\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-471.png 595w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-471-300x238.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-471-400x318.png 400w\" sizes=\"auto, (max-width: 595px) 100vw, 595px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"217\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-472.gif\" alt=\"\" class=\"wp-image-542954\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"222\" height=\"145\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-473.png\" alt=\"\" class=\"wp-image-542955\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"555\" height=\"298\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-474.png\" alt=\"\" class=\"wp-image-542956\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-474.png 555w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-474-300x161.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-474-400x215.png 400w\" sizes=\"auto, (max-width: 555px) 100vw, 555px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.29 Page No: 19.158<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-475.gif\" alt=\"\" class=\"wp-image-542957\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"454\" height=\"652\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-476.png\" alt=\"\" class=\"wp-image-542958\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-476.png 454w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-476-209x300.png 209w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-476-400x574.png 400w\" sizes=\"auto, (max-width: 454px) 100vw, 454px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"428\" height=\"639\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-477.png\" alt=\"\" class=\"wp-image-542959\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-477.png 428w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-477-201x300.png 201w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-477-400x597.png 400w\" sizes=\"auto, (max-width: 428px) 100vw, 428px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"455\" height=\"252\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-478.png\" alt=\"\" class=\"wp-image-542960\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-478.png 455w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-478-300x166.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-478-400x222.png 400w\" sizes=\"auto, (max-width: 455px) 100vw, 455px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"511\" height=\"604\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-479.png\" alt=\"\" class=\"wp-image-542961\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-479.png 511w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-479-254x300.png 254w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-479-400x473.png 400w\" sizes=\"auto, (max-width: 511px) 100vw, 511px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"605\" height=\"247\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-480.png\" alt=\"\" class=\"wp-image-542962\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-480.png 605w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-480-300x122.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-480-400x163.png 400w\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"215\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-481.gif\" alt=\"\" class=\"wp-image-542963\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-482.png\" alt=\"\" class=\"wp-image-542964\" width=\"486\" height=\"499\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-482.png 671w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-482-292x300.png 292w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-482-400x411.png 400w\" sizes=\"auto, (max-width: 486px) 100vw, 486px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-483.png\" alt=\"\" class=\"wp-image-542965\" width=\"397\" height=\"289\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-483.png 630w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-483-300x219.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-483-400x291.png 400w\" sizes=\"auto, (max-width: 397px) 100vw, 397px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"353\" height=\"644\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-484.png\" alt=\"\" class=\"wp-image-542966\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-484.png 353w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-484-164x300.png 164w\" sizes=\"auto, (max-width: 353px) 100vw, 353px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"273\" height=\"190\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-485.png\" alt=\"\" class=\"wp-image-542967\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"515\" height=\"638\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-486.png\" alt=\"\" class=\"wp-image-542968\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-486.png 515w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-486-242x300.png 242w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-486-400x496.png 400w\" sizes=\"auto, (max-width: 515px) 100vw, 515px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"581\" height=\"185\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-487.png\" alt=\"\" class=\"wp-image-542969\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-487.png 581w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-487-300x96.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-487-400x127.png 400w\" sizes=\"auto, (max-width: 581px) 100vw, 581px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"264\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-488.gif\" alt=\"\" class=\"wp-image-542970\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"457\" height=\"633\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-489.png\" alt=\"\" class=\"wp-image-542971\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-489.png 457w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-489-217x300.png 217w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-489-400x554.png 400w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"169\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-490.png\" alt=\"\" class=\"wp-image-542972\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-490.png 446w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-490-300x114.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-490-400x152.png 400w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"457\" height=\"629\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-491.png\" alt=\"\" class=\"wp-image-542973\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-491.png 457w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-491-218x300.png 218w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-491-400x551.png 400w\" sizes=\"auto, (max-width: 457px) 100vw, 457px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"425\" height=\"606\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-492.png\" alt=\"\" class=\"wp-image-542974\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-492.png 425w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-492-210x300.png 210w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-492-400x570.png 400w\" sizes=\"auto, (max-width: 425px) 100vw, 425px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"569\" height=\"645\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-493.png\" alt=\"\" class=\"wp-image-542975\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-493.png 569w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-493-265x300.png 265w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-493-400x453.png 400w\" sizes=\"auto, (max-width: 569px) 100vw, 569px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"579\" height=\"249\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-494.png\" alt=\"\" class=\"wp-image-542976\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-494.png 579w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-494-300x129.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-494-400x172.png 400w\" sizes=\"auto, (max-width: 579px) 100vw, 579px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"67\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-495.png\" alt=\"\" class=\"wp-image-542977\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-495.png 602w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-495-300x33.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-495-600x67.png 600w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-495-400x45.png 400w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"243\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-496.gif\" alt=\"\" class=\"wp-image-542978\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"454\" height=\"641\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-497.png\" alt=\"\" class=\"wp-image-542979\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-497.png 454w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-497-212x300.png 212w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-497-400x565.png 400w\" sizes=\"auto, (max-width: 454px) 100vw, 454px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-498.png\" alt=\"\" class=\"wp-image-542980\" width=\"297\" height=\"423\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-498.png 633w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-498-211x300.png 211w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-498-400x569.png 400w\" sizes=\"auto, (max-width: 297px) 100vw, 297px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"222\" height=\"279\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-499.png\" alt=\"\" class=\"wp-image-542981\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"507\" height=\"650\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-500.png\" alt=\"\" class=\"wp-image-542982\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-500.png 507w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-500-234x300.png 234w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-500-400x513.png 400w\" sizes=\"auto, (max-width: 507px) 100vw, 507px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"604\" height=\"200\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-501.png\" alt=\"\" class=\"wp-image-542983\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-501.png 604w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-501-300x99.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-501-600x200.png 600w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-501-400x132.png 400w\" sizes=\"auto, (max-width: 604px) 100vw, 604px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"606\" height=\"161\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-502.png\" alt=\"\" class=\"wp-image-542984\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-502.png 606w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-502-300x80.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-502-400x106.png 400w\" sizes=\"auto, (max-width: 606px) 100vw, 606px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.30 Page No: 19.176<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"202\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-503.gif\" alt=\"\" class=\"wp-image-542985\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"605\" height=\"634\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-504.png\" alt=\"\" class=\"wp-image-542986\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-504.png 605w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-504-286x300.png 286w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-504-400x419.png 400w\" sizes=\"auto, (max-width: 605px) 100vw, 605px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"585\" height=\"633\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-505.png\" alt=\"\" class=\"wp-image-542987\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-505.png 585w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-505-277x300.png 277w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-505-400x433.png 400w\" sizes=\"auto, (max-width: 585px) 100vw, 585px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"461\" height=\"88\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-506.png\" alt=\"\" class=\"wp-image-542988\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-506.png 461w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-506-300x57.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-506-400x76.png 400w\" sizes=\"auto, (max-width: 461px) 100vw, 461px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-507.gif\" alt=\"\" class=\"wp-image-542990\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"616\" height=\"632\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-508.png\" alt=\"\" class=\"wp-image-542991\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-508.png 616w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-508-292x300.png 292w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-508-400x410.png 400w\" sizes=\"auto, (max-width: 616px) 100vw, 616px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"554\" height=\"165\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-509.png\" alt=\"\" class=\"wp-image-542992\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-509.png 554w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-509-300x89.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-509-400x119.png 400w\" sizes=\"auto, (max-width: 554px) 100vw, 554px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"547\" height=\"638\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-510.png\" alt=\"\" class=\"wp-image-542993\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-510.png 547w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-510-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-510-400x467.png 400w\" sizes=\"auto, (max-width: 547px) 100vw, 547px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"506\" height=\"249\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-511.png\" alt=\"\" class=\"wp-image-542994\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-511.png 506w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-511-300x148.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-511-400x197.png 400w\" sizes=\"auto, (max-width: 506px) 100vw, 506px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"574\" height=\"146\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-512.png\" alt=\"\" class=\"wp-image-542995\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-512.png 574w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-512-300x76.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-512-400x102.png 400w\" sizes=\"auto, (max-width: 574px) 100vw, 574px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"582\" height=\"214\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-513.png\" alt=\"\" class=\"wp-image-542996\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-513.png 582w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-513-300x110.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-513-400x147.png 400w\" sizes=\"auto, (max-width: 582px) 100vw, 582px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"169\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-514.gif\" alt=\"\" class=\"wp-image-542997\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"633\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-515.png\" alt=\"\" class=\"wp-image-542998\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-515.png 609w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-515-289x300.png 289w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-515-400x416.png 400w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"607\" height=\"625\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-516.png\" alt=\"\" class=\"wp-image-542999\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-516.png 607w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-516-291x300.png 291w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-516-400x412.png 400w\" sizes=\"auto, (max-width: 607px) 100vw, 607px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"597\" height=\"290\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-517.png\" alt=\"\" class=\"wp-image-543000\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-517.png 597w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-517-300x146.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-517-400x194.png 400w\" sizes=\"auto, (max-width: 597px) 100vw, 597px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"583\" height=\"557\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-518.png\" alt=\"\" class=\"wp-image-543001\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-518.png 583w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-518-300x287.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-518-400x382.png 400w\" sizes=\"auto, (max-width: 583px) 100vw, 583px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-519.gif\" alt=\"\" class=\"wp-image-543002\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"607\" height=\"634\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-520.png\" alt=\"\" class=\"wp-image-543003\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-520.png 607w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-520-287x300.png 287w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-520-400x418.png 400w\" sizes=\"auto, (max-width: 607px) 100vw, 607px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"608\" height=\"623\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-521-1.png\" alt=\"\" class=\"wp-image-543004\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-521-1.png 608w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-521-1-293x300.png 293w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-521-1-400x410.png 400w\" sizes=\"auto, (max-width: 608px) 100vw, 608px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"598\" height=\"224\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-522.png\" alt=\"\" class=\"wp-image-543005\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-522.png 598w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-522-300x112.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-522-400x150.png 400w\" sizes=\"auto, (max-width: 598px) 100vw, 598px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"582\" height=\"620\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-523.png\" alt=\"\" class=\"wp-image-543006\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-523.png 582w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-523-282x300.png 282w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-523-400x426.png 400w\" sizes=\"auto, (max-width: 582px) 100vw, 582px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"130\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-524.gif\" alt=\"\" class=\"wp-image-543007\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"609\" height=\"641\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-525.png\" alt=\"\" class=\"wp-image-543008\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-525.png 609w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-525-285x300.png 285w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-525-400x421.png 400w\" sizes=\"auto, (max-width: 609px) 100vw, 609px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"898\" height=\"904\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526.png\" alt=\"\" class=\"wp-image-543009\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526.png 898w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526-298x300.png 298w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526-150x150.png 150w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526-768x773.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526-200x200.png 200w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-526-400x403.png 400w\" sizes=\"auto, (max-width: 898px) 100vw, 898px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"602\" height=\"214\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-527.png\" alt=\"\" class=\"wp-image-543010\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-527.png 602w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-527-300x107.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-527-600x214.png 600w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-527-400x142.png 400w\" sizes=\"auto, (max-width: 602px) 100vw, 602px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"580\" height=\"640\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-528.png\" alt=\"\" class=\"wp-image-543011\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-528.png 580w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-528-272x300.png 272w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-528-400x441.png 400w\" sizes=\"auto, (max-width: 580px) 100vw, 580px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"291\" height=\"47\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-529.png\" alt=\"\" class=\"wp-image-543012\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.31 Page No: 19.190<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"176\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-530.gif\" alt=\"\" class=\"wp-image-543013\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<p>The given equation can be written as,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-531.png\" alt=\"\" class=\"wp-image-543014\" width=\"208\" height=\"548\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-531.png 354w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-531-114x300.png 114w\" sizes=\"auto, (max-width: 208px) 100vw, 208px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"126\" height=\"41\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-532-1.gif\" alt=\"\" class=\"wp-image-543016\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"348\" height=\"613\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-533.png\" alt=\"\" class=\"wp-image-543017\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-533.png 348w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-533-170x300.png 170w\" sizes=\"auto, (max-width: 348px) 100vw, 348px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-534.png\" alt=\"\" class=\"wp-image-543018\" width=\"316\" height=\"283\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-534.png 744w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-534-300x269.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-534-400x359.png 400w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/figure>\n\n\n\n<p>Now, substituting t as x \u2013 1\/x and z as x + 1\/x we have<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-535.png\" alt=\"\" class=\"wp-image-543019\" width=\"351\" height=\"96\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-535.png 623w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-535-300x82.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-535-400x110.png 400w\" sizes=\"auto, (max-width: 351px) 100vw, 351px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-536.gif\" alt=\"\" class=\"wp-image-543020\" width=\"138\" height=\"47\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-537.png\" alt=\"\" class=\"wp-image-543021\" width=\"238\" height=\"347\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-537.png 588w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-537-206x300.png 206w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-537-400x583.png 400w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"164\" height=\"43\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-538.gif\" alt=\"\" class=\"wp-image-543022\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-540.png\" alt=\"\" class=\"wp-image-543023\" width=\"365\" height=\"504\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-540.png 725w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-540-217x300.png 217w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-540-400x553.png 400w\" sizes=\"auto, (max-width: 365px) 100vw, 365px\" \/><\/figure>\n\n\n\n<p>We get,<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-541.png\" alt=\"\" class=\"wp-image-543024\" width=\"326\" height=\"144\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-541.png 525w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-541-300x132.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-541-400x176.png 400w\" sizes=\"auto, (max-width: 326px) 100vw, 326px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"167\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-542.gif\" alt=\"\" class=\"wp-image-543025\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"329\" height=\"612\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-543.png\" alt=\"\" class=\"wp-image-543026\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-543.png 329w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-543-161x300.png 161w\" sizes=\"auto, (max-width: 329px) 100vw, 329px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-544.png\" alt=\"\" class=\"wp-image-543027\" width=\"307\" height=\"129\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-544.png 504w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-544-300x126.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-544-400x168.png 400w\" sizes=\"auto, (max-width: 307px) 100vw, 307px\" \/><\/figure>\n\n\n\n<h4 class=\"wp-block-heading\">Exercise 19.32 Page No: 19.196<\/h4>\n\n\n\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"192\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-545.gif\" alt=\"\" class=\"wp-image-543028\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-546.png\" alt=\"\" class=\"wp-image-543029\" width=\"237\" height=\"247\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-546.png 448w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-546-288x300.png 288w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-546-400x416.png 400w\" sizes=\"auto, (max-width: 237px) 100vw, 237px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"203\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-547-1.gif\" alt=\"\" class=\"wp-image-543030\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"389\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-548.png\" alt=\"\" class=\"wp-image-543031\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-548.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-548-231x300.png 231w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"229\" height=\"127\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-549.png\" alt=\"\" class=\"wp-image-543032\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"46\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-550.gif\" alt=\"\" class=\"wp-image-543033\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"362\" height=\"569\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-551.png\" alt=\"\" class=\"wp-image-543034\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-551.png 362w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-551-191x300.png 191w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"304\" height=\"171\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-552.png\" alt=\"\" class=\"wp-image-543035\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-552.png 304w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-552-300x169.png 300w\" sizes=\"auto, (max-width: 304px) 100vw, 304px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"48\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-553.gif\" alt=\"\" class=\"wp-image-543036\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"449\" height=\"610\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554.png\" alt=\"\" class=\"wp-image-543037\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554.png 449w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554-221x300.png 221w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554-400x543.png 400w\" sizes=\"auto, (max-width: 449px) 100vw, 449px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554a.png\" alt=\"\" class=\"wp-image-543038\" width=\"402\" height=\"278\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554a.png 848w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554a-300x208.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554a-768x533.png 768w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-554a-400x277.png 400w\" sizes=\"auto, (max-width: 402px) 100vw, 402px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-555.png\" alt=\"\" class=\"wp-image-543039\" width=\"390\" height=\"253\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-555.png 653w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-555-300x195.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-555-400x260.png 400w\" sizes=\"auto, (max-width: 390px) 100vw, 390px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"193\" height=\"45\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-556.gif\" alt=\"\" class=\"wp-image-543040\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\"\/><\/figure>\n\n\n\n<p><strong>Solution:<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-557-1.png\" alt=\"\" class=\"wp-image-543042\" width=\"316\" height=\"370\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-557-1.png 515w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-557-1-257x300.png 257w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-557-1-400x468.png 400w\" sizes=\"auto, (max-width: 316px) 100vw, 316px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-558.png\" alt=\"\" class=\"wp-image-543043\" width=\"277\" height=\"259\" title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" srcset=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-558.png 441w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-558-300x281.png 300w, https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-558-400x375.png 400w\" sizes=\"auto, (max-width: 277px) 100vw, 277px\" \/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-rd-sharma-solutions-for-class-12-maths-chapter-19-download-pdf\">RD Sharma Solutions for Class 12 Maths Chapter 19:&nbsp;<strong>Download PDF<\/strong><\/h2>\n\n\n\n<p>RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals<\/p>\n\n\n\n<p><a href=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/RD-Sharma-Solutions-for-Class-12-Maths-Chapter-19\u2013Indefinite-Integrals.pdf\" target=\"_blank\" rel=\"noreferrer noopener\"><strong>Download PDF<\/strong>: RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals PDF<\/a><\/p>\n\n\n\n<h2 class=\"wp-block-heading\" id=\"h-chapterwise-rd-sharma-solutions-for-class-12-maths\"><strong>Chapterwise RD Sharma Solutions for Class 12&nbsp;Maths :<\/strong><\/h2>\n\n\n\n<ul class=\"wp-block-list\">\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-1-relation\/\">Chapter 1\u2013Relation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-2-functions\/\">Chapter 2\u2013Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-3-binary-operations\/\">Chapter 3\u2013Binary Operations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-4-inverse-trigonometric-functions\/\">Chapter 4\u2013Inverse Trigonometric Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-5-algebra-of-matrices\/\">Chapter 5\u2013Algebra of Matrices<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-6-determinants\/\">Chapter 6\u2013Determinants<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-7-adjoint-and-inverse-of-a-matrix\/\">Chapter 7\u2013Adjoint and Inverse of a Matrix<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-8-solution-of-simultaneous-linear-equations\/\">Chapter 8\u2013Solution of Simultaneous Linear Equations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-9-continuity\/\">Chapter 9\u2013Continuity<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-10-differentiability\/\">Chapter 10\u2013Differentiability<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-11-differentiation\/\">Chapter 11\u2013Differentiation<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-12-higher-order-derivatives\/\">Chapter 12\u2013Higher Order Derivatives<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-13-derivatives-as-a-rate-measurer\/\">Chapter 13\u2013Derivatives as a Rate Measurer<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-14-differentials-errors-and-approximations\/\">Chapter 14\u2013Differentials, Errors and Approximations<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-15-mean-value-theorems\/\">Chapter 15\u2013Mean Value Theorems<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-16-tangents-and-normals\/\">Chapter 16\u2013Tangents and Normals<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-17-increasing-and-decreasing-functions\/\">Chapter 17\u2013Increasing and Decreasing Functions<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-18-maxima-and-minima\/\">Chapter 18\u2013Maxima and Minima<\/a><\/li>\n\n\n\n<li><a href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\">Chapter 19\u2013Indefinite Integrals<\/a><\/li>\n<\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">About RD Sharma<\/h2>\n\n\n\n<p>RD Sharma i<em>sn&#8217;t the kind of author you&#8217;d bump into at lit fests. But his bestselling books have helped many&nbsp;<\/em>CBSE<em>&nbsp;students lose their dread of&nbsp;<\/em>maths<em>. Sunday Times profiles the tutor turned internet star<\/em><br>He dreams of algorithms that would give most people nightmares. And, spends every waking hour thinking of ways to explain concepts like &#8216;series solution of linear differential equations&#8217;. Meet Dr&nbsp;Ravi Dutt Sharma&nbsp;\u2014&nbsp;mathematics&nbsp;teacher and author of 25 reference books \u2014 whose name evokes as much awe as the subject he teaches. And though students have used his thick tomes for the last 31 years to ace the dreaded maths exam, it&#8217;s only recently that a spoof video turned the tutor into a YouTube star.<\/p>\n\n\n\n<p>R D Sharma had a good laugh but said he shared little with his on-screen persona except for the love for maths. &#8220;I like to spend all my time thinking and writing about maths problems. I find it relaxing,&#8221; he says. When he is not writing books explaining mathematical concepts for classes 6 to 12 and engineering students, Sharma is busy dispensing his duty as vice-principal and head of department of science and humanities at Delhi government&#8217;s Guru Nanak Dev Institute of Technology.<\/p>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">RD Sharma Solutions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/ncert-class-xii\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">NCERT Class 12 Solutions<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-background wp-element-button\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-class-12\/\" style=\"background-color:#cd5c5c\" target=\"_blank\" rel=\"noreferrer noopener\">RD Sharma Class 12 <strong>Solutions<\/strong><\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Class 12: Maths Chapter 19 solutions. Complete Class 12 Maths Chapter 19 Notes. RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals RD Sharma 12th Maths Chapter 19, Class 12 Maths Chapter 19 solutions Exercise 19.1 Page No: 19.4 1. Evaluate the following integrals: Solution: Given Solution: Given Solution: Given Solution: Given Solution: Given [&hellip;]<\/p>\n","protected":false},"author":302,"featured_media":542470,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"newspack_featured_image_position":"","newspack_post_subtitle":"","newspack_article_summary_title":"Overview:","newspack_article_summary":"","newspack_hide_updated_date":false,"newspack_show_updated_date":false,"footnotes":""},"categories":[1411,25],"tags":[1961],"boards":[],"class_list":["post-542467","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-book-solutions","category-class-12","tag-rd-sharma-solutions-vol-1","entry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.0 (Yoast SEO v27.1.1) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>RD Sharma Solutions for Class 12, maths Chapter 19 - IndCareer Schools<\/title>\n<meta name=\"description\" content=\"RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals | Browse Class 12 Maths Chapters RD Sharma books - IndCareer Schools\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals\" \/>\n<meta property=\"og:description\" content=\"Class 12: Maths Chapter 19 solutions. Complete Class 12 Maths Chapter 19 Notes. RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals RD\" \/>\n<meta property=\"og:url\" content=\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\" \/>\n<meta property=\"og:site_name\" content=\"IndCareer Schools\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/indcareer\" \/>\n<meta property=\"article:published_time\" content=\"2021-09-28T10:35:35+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2022-12-26T09:40:30+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/class12-m19.png\" \/>\n\t<meta property=\"og:image:width\" content=\"1200\" \/>\n\t<meta property=\"og:image:height\" content=\"675\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/png\" \/>\n<meta name=\"author\" content=\"Pooja\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@indcareer\" \/>\n<meta name=\"twitter:site\" content=\"@indcareer\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Pooja\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"118 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\"},\"author\":{\"name\":\"Pooja\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/#\/schema\/person\/d6945cf059726f162259ba738092301e\"},\"headline\":\"RD Sharma Solutions for Class 12 Maths Chapter 19\u2013Indefinite Integrals\",\"datePublished\":\"2021-09-28T10:35:35+00:00\",\"dateModified\":\"2022-12-26T09:40:30+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\"},\"wordCount\":931,\"publisher\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/#organization\"},\"image\":{\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/#primaryimage\"},\"thumbnailUrl\":\"https:\/\/www.indcareer.com\/schools\/wp-content\/uploads\/2021\/09\/class12-m19.png\",\"keywords\":[\"RD Sharma Solutions Vol 1\"],\"articleSection\":[\"Book Solutions\",\"Class 12\"],\"inLanguage\":\"en-US\"},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\",\"url\":\"https:\/\/www.indcareer.com\/schools\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals\/\",\"name\":\"RD Sharma Solutions for Class 12, maths Chapter 19 - 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Complete Class 12 Maths Chapter 19 Notes. 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