{"id":850,"date":"2022-08-30T15:08:13","date_gmt":"2022-08-30T15:08:13","guid":{"rendered":"https:\/\/unknownerror.org\/index.php\/2013\/11\/09\/when-you-integrate-1-x-why-dont-you-get-x0-0-collection-of-common-programming-errors\/"},"modified":"2022-08-30T15:08:13","modified_gmt":"2022-08-30T15:08:13","slug":"when-you-integrate-1-x-why-dont-you-get-x0-0-collection-of-common-programming-errors","status":"publish","type":"post","link":"https:\/\/unknownerror.org\/index.php\/2022\/08\/30\/when-you-integrate-1-x-why-dont-you-get-x0-0-collection-of-common-programming-errors\/","title":{"rendered":"When you integrate 1\/x , why dont you get -(x^0)\/0?-Collection of common programming errors"},"content":{"rendered":"<ul>\n<li>Because integrating a function is anti-differentiation, and the derivative of ln(x) is 1\/x: y = ln(x) e^y = x e^y * dy = dx dy \/ dx = 1 \/ e^y\n<p>dy \/ dx = 1 \/ x<\/p>\n<\/li>\n<li>The integration of 1\/x^a for a not 1 is 1\/(1-a) * x^(1-a). If you look at the primitive F_a such that F_a(1) = 1, then F_a(x) = ( x^(1-a) &#8211; 1) \/ (1-a).\n<p>If now you plug in a = 1, you get non sense but if you make a tend to 1, then you obtain a derivative with respect to a, that is ln (x).<\/p>\n<\/li>\n<\/ul>\n<p id=\"rop\"><small>Originally posted 2013-11-09 22:48:57. <\/small><\/p>","protected":false},"excerpt":{"rendered":"<p>Because integrating a function is anti-differentiation, and the derivative of ln(x) is 1\/x: y = ln(x) e^y = x e^y * dy = dx dy \/ dx = 1 \/ e^y dy \/ dx = 1 \/ x The integration of 1\/x^a for a not 1 is 1\/(1-a) * x^(1-a). If you look at the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-850","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts\/850","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/comments?post=850"}],"version-history":[{"count":0,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/posts\/850\/revisions"}],"wp:attachment":[{"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/categories?post=850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/unknownerror.org\/index.php\/wp-json\/wp\/v2\/tags?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}