## [Maxima-bugs] [ maxima-Bugs-1374700 ] integrate((1+tan(x)^2)/tan(x),x);

 [Maxima-bugs] [ maxima-Bugs-1374700 ] integrate((1+tan(x)^2)/tan(x),x); From: SourceForge.net - 2006-02-13 18:07:03 ```Bugs item #1374700, was opened at 2005-12-06 13:41 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1374700&group_id=4933 Please note that this message will contain a full copy of the comment thread, including the initial issue submission, for this request, not just the latest update. Category: Xmaxima Group: None Status: Open Resolution: None Priority: 5 Submitted By: Nobody/Anonymous (nobody) Assigned to: Nobody/Anonymous (nobody) Summary: integrate((1+tan(x)^2)/tan(x),x); Initial Comment: Non-real result ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-02-13 13:07 Message: Logged In: YES user_id=28849 This integral is transformed to cos(x)/sin(x)*(sin(x)^2/cos(x)^2+1). Then maxima uses the substitution y=sin(x) to get 1/y*(y^2/(1-y^2)+1. However: integrate(1/y*(y^2/(1-y^2)+1),y) -> log(y)-log(y^2-1)/2. But integrate(expand(1/y*(y^2/(1-y^2)+1)),y) -> log(y)-log(1-y^2)/2. The former is wrong for our integration problem; the latter would produce the desired answer. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1374700&group_id=4933 ```