{"id":666483,"date":"2023-08-08T14:54:08","date_gmt":"2023-08-08T09:24:08","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/?p=666483"},"modified":"2025-07-25T16:50:15","modified_gmt":"2025-07-25T11:20:15","slug":"integral-formulas","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/","title":{"rendered":"Integral formulas"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 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\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" 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: #999;color:#999\" 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\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Introduction_to_Integral_formulas\" title=\"Introduction to Integral formulas\">Introduction to Integral formulas<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integral_formulae_for_algebraic_functions\" title=\"Integral formulae for algebraic functions\">Integral formulae for algebraic functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Rules_for_integration\" title=\"Rules for integration:\">Rules for integration:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Power_Rule\" title=\"Power Rule:\">Power Rule:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Constant_Multiple_Rule\" title=\"Constant Multiple Rule:\">Constant Multiple Rule:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#SumDifference_Rule\" title=\"Sum\/Difference Rule:\">Sum\/Difference Rule:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_by_Parts\" title=\"Integration by Parts:\">Integration by Parts:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integral_formulae_for_Trigonometric_functions\" title=\"Integral formulae for Trigonometric functions:\">Integral formulae for Trigonometric functions:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_of_hyperbolic_function\" title=\"Integration of hyperbolic function\">Integration of hyperbolic function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_of_rational_functions\" title=\"Integration of rational functions\">Integration of rational functions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_of_irrational_function\" title=\"Integration of irrational function\">Integration of irrational function<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Special_integrals\" title=\"Special integrals\">Special integrals<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_by_substitution_related_formula\" title=\"Integration by substitution related formula\">Integration by substitution related formula<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_formula_by_partial_fractions\" title=\"Integration formula by partial fractions\">Integration formula by partial fractions<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Integration_by_parts\" title=\"Integration by parts:\">Integration by parts:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Some_Integral_formulas_using_integration_by_parts\" title=\"Some Integral formulas using integration by parts\">Some Integral formulas using integration by parts<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Solved_examples_which_including_integration_formulas\" title=\"Solved examples which including integration formulas\">Solved examples which including integration formulas<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Frequently_asked_questions_on_Integration_formulas\" title=\"Frequently asked questions on Integration formulas\">Frequently asked questions on Integration formulas<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#What_is_the_integration_formula\" title=\"What is the integration formula? \">What is the integration formula? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#What_is_dx_in_integration\" title=\"What is dx in integration?\">What is dx in integration?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#What_is_called_integration\" title=\"What is called integration?\">What is called integration?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#Why_is_integration_used\" title=\"Why is integration used? \">Why is integration used? <\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/integral-formulas\/#What_are_the_rules_of_integration\" title=\"What are the rules of integration?\">What are the rules of integration?<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Introduction_to_Integral_formulas\"><\/span>Introduction to Integral formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Integral formulae are key tools in calculus, used to calculate areas under curves, volumes of solids, and a variety of other things. Calculus&#8217; basic theorem relates integrals with derivatives, making integral evaluation easier. The power rule, substitution rule, and integration by parts are all important formulae. Understanding and using these principles enables pupils to solve a wide range of mathematical problems.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integral_formulae_for_algebraic_functions\"><\/span>Integral formulae for algebraic functions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666484 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-algebraic-functions-.png\" alt=\"Integral formulae for algebraic functions \" width=\"297\" height=\"531\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-algebraic-functions-.png 297w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-algebraic-functions--168x300.png 168w\" sizes=\"(max-width: 297px) 100vw, 297px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Rules_for_integration\"><\/span>Rules for integration:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Here are some common integration formulas for algebraic functions:<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Power_Rule\"><\/span>Power Rule:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u222b x^n dx = (x^(n+1))\/(n+1) + C, where n \u2260 -1.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Constant_Multiple_Rule\"><\/span>Constant Multiple Rule:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u222b k * f(x) dx = k * \u222b f(x) dx, where k is a constant.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"SumDifference_Rule\"><\/span>Sum\/Difference Rule:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u222b [f(x) + g(x)] dx = \u222b f(x) dx + \u222b g(x) dx.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Integration_by_Parts\"><\/span>Integration by Parts:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<ul>\n<li>\u222b u dv = u * v &#8211; \u222b v du, where u and v are differentiable functions.<\/li>\n<\/ul>\n<p>These formulas are just a few examples of the wide range of algebraic functions that can be integrated. Integrating more complex functions may require using multiple techniques and approaches..<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integral_formulae_for_Trigonometric_functions\"><\/span>Integral formulae for Trigonometric functions:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666486 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-Trigonometric-functions.png\" alt=\"Integral formulae for Trigonometric functions\" width=\"553\" height=\"589\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-Trigonometric-functions.png 553w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulae-for-Trigonometric-functions-282x300.png 282w\" sizes=\"(max-width: 553px) 100vw, 553px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_of_hyperbolic_function\"><\/span>Integration of hyperbolic function<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666487 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-hyperbolic-function.png\" alt=\"Integration of hyperbolic function\" width=\"402\" height=\"577\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-hyperbolic-function.png 402w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-hyperbolic-function-209x300.png 209w\" sizes=\"(max-width: 402px) 100vw, 402px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_of_rational_functions\"><\/span>Integration of rational functions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666490 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-rational-functions-1.png\" alt=\"Integration of rational functions \" width=\"340\" height=\"379\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-rational-functions-1.png 340w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-rational-functions-1-269x300.png 269w\" sizes=\"(max-width: 340px) 100vw, 340px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_of_irrational_function\"><\/span>Integration of irrational function<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666489 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-irrational-function-.png\" alt=\"Integration of irrational function\" width=\"612\" height=\"805\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-irrational-function-.png 612w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-of-irrational-function--228x300.png 228w\" sizes=\"(max-width: 612px) 100vw, 612px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Special_integrals\"><\/span>Special integrals<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666491 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Special-integrals-.png\" alt=\"Special integrals \" width=\"427\" height=\"196\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Special-integrals-.png 427w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Special-integrals--300x138.png 300w\" sizes=\"(max-width: 427px) 100vw, 427px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_by_substitution_related_formula\"><\/span>Integration by substitution related formula<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666492 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-by-substitution-related-formula-.png\" alt=\"Integration by substitution related formula \" width=\"577\" height=\"481\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-by-substitution-related-formula-.png 577w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-by-substitution-related-formula--300x250.png 300w\" sizes=\"(max-width: 577px) 100vw, 577px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_formula_by_partial_fractions\"><\/span>Integration formula by partial fractions<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666494 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-by-partial-fractions-1-1.png\" alt=\"Integration formula by partial fractions \" width=\"499\" height=\"505\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-by-partial-fractions-1-1.png 499w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-by-partial-fractions-1-1-296x300.png 296w\" sizes=\"(max-width: 499px) 100vw, 499px\" \/><\/p>\n<p><strong>Also read: <span style=\"color: #0000ff;\"><a class=\"row-title\" style=\"color: #0000ff;\" href=\"https:\/\/infinitylearn.com\/surge\/formulas\/math-formulas\/\" target=\"_blank\" rel=\"noopener\" aria-label=\"\u201cMath Formulas\u201d (Edit)\">Math Formulas<\/a><\/span><\/strong><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Integration_by_parts\"><\/span>Integration by parts:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><strong>If  <em>f(x), g(x)<\/em> are any two functions, then<\/strong><\/p>\n<p><em>\u222bf(x).g(x)dx = f(x)\u222bg(x)dx &#8211; \u222bf'(x)\u222bg(x)dxdx<\/em><\/p>\n<p><strong>Proper choice of first and second function<\/strong><\/p>\n<ul>\n<li>The first function is the function which comes first in the word ILATE<\/li>\n<li>If one of the two functions is not directly integrable, then take this function as the first function.<\/li>\n<li>If one of the function is not directly integrable, and there is no other function, then unity is taken as the second function.<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Some_Integral_formulas_using_integration_by_parts\"><\/span>Some Integral formulas using integration by parts<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666495 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulas-using-integration-by-parts.png\" alt=\"Integral formulas using integration by parts\" width=\"370\" height=\"277\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulas-using-integration-by-parts.png 370w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integral-formulas-using-integration-by-parts-300x225.png 300w\" sizes=\"(max-width: 370px) 100vw, 370px\" \/><\/p>\n<p>Integration formula for inverse trigonometric functions<\/p>\n<p><img loading=\"lazy\" class=\"alignnone wp-image-666496 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-for-inverse-trigonometric-functions.png\" alt=\"Integration formula for inverse trigonometric functions\" width=\"333\" height=\"283\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-for-inverse-trigonometric-functions.png 333w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2023\/08\/Integration-formula-for-inverse-trigonometric-functions-300x255.png 300w\" sizes=\"(max-width: 333px) 100vw, 333px\" \/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Solved_examples_which_including_integration_formulas\"><\/span>Solved examples which including integration formulas<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Solve some examples using the integration formulas mentioned earlier.<\/p>\n<p><strong>Example 1: \u222b (3x^2 + 2x + 1) dx<\/strong><\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (3x^2) dx = (3 * x^(2+1))\/(2+1) + C<\/p>\n<p>= (3\/3) * x^3 + C<\/p>\n<p>= x^3 + C.<\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (2x) dx = (2 * x^(1+1))\/(1+1) + C<\/p>\n<p>= x^2 + C.<\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (1) dx = x + C.<\/p>\n<p>Putting it all together:<\/p>\n<p>\u222b (3x^2 + 2x + 1) dx = x^3 + x^2 + x + C.<\/p>\n<p><strong>Example 2: \u222b (e^x + 5sin(x)) dx<\/strong><\/p>\n<p>Using the Exponential Integral:<\/p>\n<p>\u222b e^x dx = e^x + C.<\/p>\n<p>Using the Trigonometric Integral:<\/p>\n<p>\u222b sin(x) dx = -cos(x) + C.<\/p>\n<p>Since the integral of a sum is the sum of integrals:<\/p>\n<p>\u222b (e^x + 5sin(x)) dx = (e^x + C) + 5*(-cos(x) + C)<\/p>\n<p>= e^x &#8211; 5cos(x) + C.<\/p>\n<p><strong>Example 3: \u222b (x^3 + 2x^2 &#8211; 2x + 5) dx<\/strong><\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (x^3) dx = (x^(3+1))\/(3+1) + C = (1\/4) * x^4 + C.<\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (2x^2) dx = (2 * x^(2+1))\/(2+1) + C = (2\/3) * x^3 + C.<\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (-2x) dx = -2 * (x^(1+1))\/(1+1) + C = -x^2 + C.<\/p>\n<p>Using the Power Rule:<\/p>\n<p>\u222b (5) dx = 5 * x + C.<\/p>\n<p>Putting it all together:<\/p>\n<p>\u222b (x^3 + 2x^2 &#8211; 2x + 5) dx = (1\/4) * x^4 + (2\/3) * x^3 &#8211; x^2 + 5x + C.<\/p>\n<p>These are just a few examples to illustrate the use of integration formulas. Remember, integration can involve more complex functions and may require multiple steps or special techniques in some cases.<\/p>\n<div class=\"table-responsive\">\n<table class=\"table table-bordered table-striped\" style=\"width: 86.9134%; height: 876px;\" cellspacing=\"0\" cellpadding=\"5\">\n<tbody>\n<tr style=\"background-color: #89cff0; color: black;\">\n<td style=\"text-align: center; height: 23px; width: 99.6479%;\" colspan=\"2\"><strong>Also Check<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/perimeter-of-rectangle\/\">Perimeter of Rectangle<\/a><\/strong><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/distance-formula\/\">Distance Formula<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><strong>Volume Of A Cylinder Formula<\/strong><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/volume-formulae\/\">Volume Formulas<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><strong>Basic Math Formulas<\/strong><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong>Circumference Formula<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><a href=\"https:\/\/infinitylearn.com\/surge\/perimeter-of-rhombus-formula\/\"><strong>Perimeter of Rhombus Formula<\/strong><\/a><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong>Rhombus Formula<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/surface-area-formulas\">Surface Area Formulas<\/a><\/strong><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/equilateral-triangle-formula\">Equilateral Triangle Formula<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 47px;\">\n<td style=\"height: 47px; width: 40.8451%; text-align: center;\"><strong>Perimeter of a Parallelogram Formula<\/strong><\/td>\n<td style=\"height: 47px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/radius-formula\">Radius Formula<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/trapezoid-formula\">Trapezoid formula<\/a><\/strong><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/diagonal-of-a-cube-formula\">Diagonal of a Cube Formula<\/a><\/strong><\/td>\n<\/tr>\n<tr style=\"height: 23px;\">\n<td style=\"height: 23px; width: 40.8451%; text-align: center;\"><\/td>\n<td style=\"height: 23px; width: 58.8028%; text-align: center;\"><strong><a href=\"https:\/\/infinitylearn.com\/surge\/percentage-increase-formula\">Percentage Increase Formula<\/a><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<h2><span class=\"ez-toc-section\" id=\"Frequently_asked_questions_on_Integration_formulas\"><\/span>Frequently asked questions on Integration formulas<span class=\"ez-toc-section-end\"><\/span><\/h2>\n\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_the_integration_formula\"><\/span>What is the integration formula? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tA mathematical statement that allows us to compute the antiderivative of a given function is known as an integration formula. When the derivative of the original function is known, it aids in determining the original function. Integration allows the computation of areas, volumes, and other important quantities in calculus by employing various integration rules and procedures.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_dx_in_integration\"><\/span>What is dx in integration?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIn integration, the symbol dx represents the differential of the variable x. It is an infinitesimal change in the independent variable x. The process of integration involves finding the antiderivative of a function with respect to x, and the 'dx' in the integral notation indicates that the integration is being performed with respect to 'x.' The 'dx' notation is used to specify the variable of integration and is a fundamental part of the integral calculus notation. It allows us to find the area under a curve, calculate accumulated quantities, and solve a wide range of mathematical problems.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_is_called_integration\"><\/span>What is called integration?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIntegration is a fundamental concept in calculus, and it refers to the process of finding the antiderivative of a function. It is the reverse operation of differentiation. When we integrate a function, we determine another function whose derivative is equal to the original function. Integration is used to calculate areas under curves, volumes of solids, and to solve various mathematical problems in physics, engineering, economics, and other fields. It plays a crucial role in understanding the behavior of functions and their cumulative effects.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"Why_is_integration_used\"><\/span>Why is integration used? <span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tIntegration is used for a variety of reasons in mathematics, science, and engineering due to its versatile applications: Area Calculation: Integration finds the area under curves, helping measure irregular regions. Volume Calculation: It determines volumes of complex 3D shapes. Accumulated Quantities: Integration calculates total change, like distance traveled, profit, or mass, based on rates of change. Physics and Engineering: Used to calculate work, energy, electric charge, fluid flow, moments of inertia, and centroids. Probability and Statistics: Employed in probability density functions and cumulative distribution functions. Differential Equations: It helps solve differential equations that model various phenomena. Economics and Finance: Used in economic models, pricing financial derivatives, and finance calculations. Signal Processing: Employed to calculate accumulated signal values over time. Optimization: It helps find maximum and minimum values of functions, aiding in optimization problems. Integration is a powerful tool, crucial for understanding real-world phenomena and solving a wide range of problems.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"sc_fs_faq sc_card \">\n\t\t\t<div>\n\t\t\t\t<h3><span class=\"ez-toc-section\" id=\"What_are_the_rules_of_integration\"><\/span>What are the rules of integration?<span class=\"ez-toc-section-end\"><\/span><\/h3>\t\t\t\t<div>\n\t\t\t\t\t\t\t\t\t\t<p>\n\t\t\t\t\t\tThe rules of integration, also known as integration techniques or methods, are essential tools in calculus used to find antiderivatives and solve integrals. Improper Integrals: Used to evaluate integrals with infinite limits or unbounded functions. These rules, along with other specialized techniques, allow us to evaluate a wide range of integrals and solve diverse mathematical problems.\t\t\t\t\t<\/p>\n\t\t\t\t<\/div>\n\t\t\t<\/div>\n\t\t<\/section>\n\t\t\n<script type=\"application\/ld+json\">\n\t{\n\t\t\"@context\": \"https:\/\/schema.org\",\n\t\t\"@type\": \"FAQPage\",\n\t\t\"mainEntity\": [\n\t\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is the integration formula? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"A mathematical statement that allows us to compute the antiderivative of a given function is known as an integration formula. When the derivative of the original function is known, it aids in determining the original function. Integration allows the computation of areas, volumes, and other important quantities in calculus by employing various integration rules and procedures.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is dx in integration?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"In integration, the symbol dx represents the differential of the variable x. It is an infinitesimal change in the independent variable x. The process of integration involves finding the antiderivative of a function with respect to x, and the 'dx' in the integral notation indicates that the integration is being performed with respect to 'x.' The 'dx' notation is used to specify the variable of integration and is a fundamental part of the integral calculus notation. It allows us to find the area under a curve, calculate accumulated quantities, and solve a wide range of mathematical problems.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What is called integration?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Integration is a fundamental concept in calculus, and it refers to the process of finding the antiderivative of a function. It is the reverse operation of differentiation. When we integrate a function, we determine another function whose derivative is equal to the original function. Integration is used to calculate areas under curves, volumes of solids, and to solve various mathematical problems in physics, engineering, economics, and other fields. It plays a crucial role in understanding the behavior of functions and their cumulative effects.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"Why is integration used? \",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"Integration is used for a variety of reasons in mathematics, science, and engineering due to its versatile applications: Area Calculation: Integration finds the area under curves, helping measure irregular regions. Volume Calculation: It determines volumes of complex 3D shapes. Accumulated Quantities: Integration calculates total change, like distance traveled, profit, or mass, based on rates of change. Physics and Engineering: Used to calculate work, energy, electric charge, fluid flow, moments of inertia, and centroids. Probability and Statistics: Employed in probability density functions and cumulative distribution functions. Differential Equations: It helps solve differential equations that model various phenomena. Economics and Finance: Used in economic models, pricing financial derivatives, and finance calculations. Signal Processing: Employed to calculate accumulated signal values over time. Optimization: It helps find maximum and minimum values of functions, aiding in optimization problems. Integration is a powerful tool, crucial for understanding real-world phenomena and solving a wide range of problems.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t,\t\t\t\t{\n\t\t\t\t\"@type\": \"Question\",\n\t\t\t\t\"name\": \"What are the rules of integration?\",\n\t\t\t\t\"acceptedAnswer\": {\n\t\t\t\t\t\"@type\": \"Answer\",\n\t\t\t\t\t\"text\": \"The rules of integration, also known as integration techniques or methods, are essential tools in calculus used to find antiderivatives and solve integrals. Improper Integrals: Used to evaluate integrals with infinite limits or unbounded functions. These rules, along with other specialized techniques, allow us to evaluate a wide range of integrals and solve diverse mathematical problems.\"\n\t\t\t\t\t\t\t\t\t}\n\t\t\t}\n\t\t\t\t\t\t]\n\t}\n<\/script>\n\n","protected":false},"excerpt":{"rendered":"<p>Introduction to Integral formulas Integral formulae are key tools in calculus, used to calculate areas under curves, volumes of solids, [&hellip;]<\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Integral formulas","_yoast_wpseo_title":"List of Integral Formulas - Rules for integration, Solved Example PDF","_yoast_wpseo_metadesc":"Integral formulas allow us to calculate definite and indefinite integrals. 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