{"id":69135,"date":"2023-09-12T17:16:00","date_gmt":"2023-09-12T11:46:00","guid":{"rendered":"https:\/\/www.kopykitab.com\/blog\/?p=69135"},"modified":"2025-07-12T12:56:20","modified_gmt":"2025-07-12T07:26:20","slug":"rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25","status":"publish","type":"post","link":"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/","title":{"rendered":"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 (Updated for 2026)"},"content":{"rendered":"\n<p><img class=\"alignnone size-full wp-image-120019\" src=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.25.png\" alt=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25\" width=\"1200\" height=\"675\" srcset=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.25.png 1200w, https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/01\/RD-Sharma-Solutions-Class-12-Chapter-19-Exercise-19.25-768x432.png 768w\" sizes=\"(max-width: 1200px) 100vw, 1200px\" \/><\/p>\n<p><strong>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25<\/strong>: Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems on a daily basis, students improve their problem solving and logical thinking skills. This is important for getting better academic grades. The main goal of <a href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-indefinite-integrals\/\" target=\"_blank\" rel=\"noopener\">RD Sharma Solutions Class 12 Maths Chapter 19<\/a> is to help students self-analyze the areas that require the most practice from the exam point of view.&nbsp;<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_47_1 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" aria-label=\"ez-toc-toggle-icon-1\"><label for=\"item-69f33fc4ed3fb\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #000000;color:#000000\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #000000;color:#000000\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-69f33fc4ed3fb\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 eztoc-visibility-hide-by-default' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-pdf\" title=\"Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF\">Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\" title=\"Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25\">Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-important-topics-from-the-chapter\" title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25: Important Topics From The Chapter\">RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25: Important Topics From The Chapter<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\" title=\"FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25\">FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#is-class-12-maths-tough\" title=\"Is Class 12 Maths tough? \">Is Class 12 Maths tough? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#can-i-download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-pdf-free\" title=\"Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF free? \">Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF free? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#how-to-get-all-the-solutions-for-class-12-maths-rd-sharma\" title=\"How to get all the solutions for Class 12 Maths RD Sharma? \">How to get all the solutions for Class 12 Maths RD Sharma? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#what-are-the-important-topics-included-in-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\" title=\"What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25? \">What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/#how-many-types-of-integrals-are-there\" title=\"How many types of integrals are there? \">How many types of integrals are there? <\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-pdf\"><\/span>Download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div id=\"example1\" style=\"text-align: justify;\">&nbsp;<\/div>\n<p style=\"text-align: justify;\"><style>\n.pdfobject-container { height: 500px;}<br \/>\n.pdfobject { border: 1px solid #666; }<br \/>\n<\/style><\/p>\n<p style=\"text-align: justify;\"><script src=\"https:\/\/www.kopykitab.com\/_utility\/js\/pdfobject.min.js\"><\/script><br><script>PDFObject.embed(\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.25.pdf\", \"#example1\");<\/script><\/p>\n<p><a href=\"https:\/\/www.kopykitab.com\/blog\/wp-content\/uploads\/2021\/08\/RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.25.pdf\">RD-Sharma-Solutions-Class-12-Maths-Chapter-19-Ex-19.25<\/a><\/p>\n<h2><span class=\"ez-toc-section\" id=\"access-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\"><\/span>Access RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<article id=\"post-57155\" class=\"post-57155 page type-page status-publish hentry\">\n<p><strong>Evaluate the following integrals:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-428.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 428\"><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-429.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 429\"><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-430.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 430\"><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-431.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 431\"><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-432.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 432\"><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-433.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 433\"><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-434.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 434\"><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-435.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 435\"><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-436.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 436\"><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-437.gif\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 437\"><\/p>\n<p><strong>Solution:<\/strong><\/p>\n<p><img title=\"RD Sharma Solutions for Class 12 Maths Chapter 19\" src=\"https:\/\/cdn1.byjus.com\/wp-content\/uploads\/2020\/11\/rd-sharma-solutions-for-class-12-maths-chapter-19-indefinite-integrals-image-438.png\" alt=\"RD Sharma Solutions for Class 12 Maths Chapter 19 Indefinite Integrals Image 438\"><\/p>\n<\/article>\n<h2><span class=\"ez-toc-section\" id=\"rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-important-topics-from-the-chapter\"><\/span>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25: Important Topics From The Chapter<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Some of the essential topics covered in&nbsp;RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 chapter are listed below.<\/p>\n<ul>\n<li>Definition of primitive or antiderivative<\/li>\n<li>Definition and meaning of indefinite integral<\/li>\n<li>Fundamental integration formulae<\/li>\n<li>Some standard results on integration along with the corollary<\/li>\n<li>Integration of trigonometric functions<\/li>\n<li>Integration of exponential functions<\/li>\n<li>Miscellaneous problems<\/li>\n<li>Geometrical interpretation of indefinite integral<\/li>\n<li>Comparison between differentiation and integration<\/li>\n<li>Methods of integration<\/li>\n<li>Integration by substitution<\/li>\n<li>Some standard results<\/li>\n<li>Evaluation of integrals by using trigonometric substitutions<\/li>\n<li>Some special integrals<\/li>\n<li>Integration by parts<\/li>\n<li>Some important integrals along with theorems<\/li>\n<li>Integration of rational algebraic functions by using partial fractions\n<ul>\n<li>When the denominator is expressible as a product of distinct linear factors<\/li>\n<li>When the denominator contains some repeating linear factors<\/li>\n<li>The denominator contains irreducible quadratic factors<\/li>\n<\/ul>\n<\/li>\n<li>Integration of some special irrational algebraic functions<\/li>\n<\/ul>\n<p>We have included all the information regarding&nbsp;<a href=\"https:\/\/www.cbse.gov.in\/\" target=\"_blank\" rel=\"noopener\">CBSE<\/a> RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25. If you have any queries feel free to ask in the comment section.&nbsp;<\/p>\n<h3><span class=\"ez-toc-section\" id=\"faq-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\"><\/span>FAQ: RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25<span class=\"ez-toc-section-end\"><\/span><\/h3>\n\n\n<div id=\"rank-math-faq\" class=\"rank-math-block\">\n<div class=\"rank-math-list \">\n<div id=\"faq-question-1629978109164\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"is-class-12-maths-tough\"><\/span>Is Class 12 Maths tough? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Some students find Maths Class 12 difficult due to the syllabus and concepts. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629978137776\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"can-i-download-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925-pdf-free\"><\/span>Can I download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF free? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Yes, you can download RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 PDF free. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629978138751\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-to-get-all-the-solutions-for-class-12-maths-rd-sharma\"><\/span>How to get all the solutions for Class 12 Maths RD Sharma? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can refer to the above article. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629978139720\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"what-are-the-important-topics-included-in-rd-sharma-solutions-class-12-maths-chapter-19-exercise-1925\"><\/span>What are the important topics included in RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>You can refer to the above article. <\/p>\n\n<\/div>\n<\/div>\n<div id=\"faq-question-1629978262725\" class=\"rank-math-list-item\">\n<h3 class=\"rank-math-question \"><span class=\"ez-toc-section\" id=\"how-many-types-of-integrals-are-there\"><\/span>How many types of integrals are there? <span class=\"ez-toc-section-end\"><\/span><\/h3>\n<div class=\"rank-math-answer \">\n\n<p>Definite and Indefinite Integrals. <\/p>\n\n<\/div>\n<\/div>\n<\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25: Solutions PDF is an important reference guide to help students score well in the Class 12 exam. By solving exercise problems on a daily basis, students improve their problem solving and logical thinking skills. This is important for getting better academic grades. The main goal &#8230; <a title=\"RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 (Updated for 2026)\" class=\"read-more\" href=\"https:\/\/www.kopykitab.com\/blog\/rd-sharma-solutions-class-12-maths-chapter-19-exercise-19-25\/\" aria-label=\"More on RD Sharma Solutions Class 12 Maths Chapter 19 Exercise 19.25 (Updated for 2026)\">Read more<\/a><\/p>\n","protected":false},"author":244,"featured_media":120019,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"fifu_image_url":"","fifu_image_alt":""},"categories":[2917,73712,73411,2985,73410],"tags":[3429,73223,73664,76756],"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69135"}],"collection":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/users\/244"}],"replies":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/comments?post=69135"}],"version-history":[{"count":5,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69135\/revisions"}],"predecessor-version":[{"id":574346,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/posts\/69135\/revisions\/574346"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media\/120019"}],"wp:attachment":[{"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/media?parent=69135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/categories?post=69135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.kopykitab.com\/blog\/wp-json\/wp\/v2\/tags?post=69135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}