{"id":144382,"date":"2018-02-20T23:50:30","date_gmt":"2018-02-20T23:50:30","guid":{"rendered":"https:\/\/writemyessayfree.com\/how-do-you-integrate-e2xsinxdx"},"modified":"2017-08-17T11:48:20","modified_gmt":"2017-08-17T11:48:20","slug":"how-do-you-integrate-e2xsinxdx","status":"publish","type":"post","link":"https:\/\/www.benedictsol.com\/blogs\/how-do-you-integrate-e2xsinxdx\/","title":{"rendered":"How do you integrate ##[(e^(2x))sinx]dx##?"},"content":{"rendered":"<p>Integrate by parts twice using ##u = e^(2x)## both times.<\/p>\n<p>After the second , you&#8217;ll have<\/p>\n<p>##int e^(2x)sinx dx = -e^(2x)cosx + 2e^(2x)sinx &#8211; 4 int e^(2x)sinx dx##<\/p>\n<p>Note that the last integral is the same as the one we want. Call it ##I## for now.<\/p>\n<p>##I = -e^(2x)cosx + 2e^(2x)sinx &#8211; 4 I##<\/p>\n<p>So ##I = 1\/5[-e^(2x)cosx + 2e^(2x)sinx] +C##<\/p>\n<p>You may rewrite \/ simplify \/ factor as you see fit.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Integrate by parts twice using ##u = e^(2x)## both times. After the second , you&#8217;ll have ##int e^(2x)sinx dx = -e^(2x)cosx + 2e^(2x)sinx &#8211; 4 int e^(2x)sinx dx## Note that the last integral is the same as the one we <a href=\"https:\/\/www.benedictsol.com\/blogs\/how-do-you-integrate-e2xsinxdx\/\" class=\"read-more\">Read More &#8230;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[],"tags":[],"class_list":["post-144382","post","type-post","status-publish","format-standard","hentry"],"_links":{"self":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/144382","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/comments?post=144382"}],"version-history":[{"count":0,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/posts\/144382\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/media?parent=144382"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/categories?post=144382"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.benedictsol.com\/blogs\/wp-json\/wp\/v2\/tags?post=144382"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}