{"id":4416,"date":"2022-06-13T07:17:00","date_gmt":"2022-06-13T07:17:00","guid":{"rendered":"https:\/\/mdr.foobrdigital.com\/?p=4416"},"modified":"2022-06-13T07:17:00","modified_gmt":"2022-06-13T07:17:00","slug":"methods-to-find-integrals","status":"publish","type":"post","link":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/2022\/06\/13\/methods-to-find-integrals\/","title":{"rendered":"Methods to Find Integrals"},"content":{"rendered":"\n<p>There are several methods adopted for finding the indefinite integrals.&nbsp;The prominent methods are:<\/p>\n\n\n\n<ul><li>Finding integrals by\u00a0integration by substitution method<\/li><li>Finding integrals by\u00a0integration by parts<\/li><li>Finding integrals by\u00a0integration by partial fractions.<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Finding Integrals by Substitution Method<\/h3>\n\n\n\n<p>A few integrals are found by the substitution method. If u is a function of x, then u&#8217; = du\/dx.<\/p>\n\n\n\n<p>\u222b f(u)u&#8217; dx = \u222b f(u)du, where u = g(x).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Finding Integrals by Integration by Parts<\/h3>\n\n\n\n<p>If two functions are of the product form,&nbsp; integrals are found by the method of integration by parts.<\/p>\n\n\n\n<p>\u222bf(x)g(x) dx = f(x)\u222b g(x) dx &#8211; \u222b (f'(x) \u222bg(x) dx) dx.&nbsp;<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Finding Integrals by Integration by Partial Fractions<\/h3>\n\n\n\n<p>Integration of rational algebraic functions whose numerator and denominator contain positive integral powers of x with constant coefficients is done by resolving them into partial fractions.<\/p>\n\n\n\n<p>To find \u222b f(x)\/g(x) dx, decompose this improper rational function to a proper rational function and then integrate.<\/p>\n\n\n\n<p>\u222bf(x)\/g(x) dx = \u222b p(x)\/q(x) + \u222b r(x)\/s(x), where g(x) = a(x) . s(x)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>There are several methods adopted for finding the indefinite integrals.&nbsp;The prominent methods are: Finding integrals by\u00a0integration by substitution method Finding integrals by\u00a0integration by parts Finding integrals by\u00a0integration by partial fractions. Finding Integrals by Substitution Method A few integrals are found by the substitution method. If u is a function of x, then u&#8217; = du\/dx. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[865],"tags":[],"_links":{"self":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4416"}],"collection":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/comments?post=4416"}],"version-history":[{"count":0,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/posts\/4416\/revisions"}],"wp:attachment":[{"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/media?parent=4416"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/categories?post=4416"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mudassirbackup.infinitycodestudio.com\/index.php\/wp-json\/wp\/v2\/tags?post=4416"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}