## [Maxima-bugs] [ maxima-Bugs-1451351 ] integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong

 [Maxima-bugs] [ maxima-Bugs-1451351 ] integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong From: SourceForge.net - 2006-03-28 04:57:19 ```Bugs item #1451351, was opened at 2006-03-16 10:11 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&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: None Group: None >Status: Closed >Resolution: Fixed Priority: 5 Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong Initial Comment: assume(kk<0,kk+1>0); integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf); Answer kk is not an integer. If you exponentialize and factor the result of the integral you get -(log(3)^2+%pi^2)/2*exp(log(3)*kk+%i*%pi*kk) Since -1 < kk < 0, exp(%i*%pi*kk) is complex. Hence, the integral of a real-valued function is complex. That's wrong. This integral uses rectzto%pi2 to evaluate it, which is a rectangle of height 2*%pi. The algorithm seems correct, but the result is clearly wrong. ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-03-27 23:57 Message: Logged In: YES user_id=28849 This should be fixed in CVS. rectzto%pi2 no longer succeeds on this integral because the exponential part is not a rational function of exp(x). The code has been enhanced to convert this integral to another form using the substitution x=log(y), which results in an integral that maxima knows how to handle. Closing this bug. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&group_id=4933 ```

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 [Maxima-bugs] [ maxima-Bugs-1451351 ] integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong From: SourceForge.net - 2006-03-16 15:11:24 ```Bugs item #1451351, was opened at 2006-03-16 10:11 Message generated for change (Tracker Item Submitted) made by Item Submitter You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&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: None Group: None Status: Open Resolution: None Priority: 5 Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong Initial Comment: assume(kk<0,kk+1>0); integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf); Answer kk is not an integer. If you exponentialize and factor the result of the integral you get -(log(3)^2+%pi^2)/2*exp(log(3)*kk+%i*%pi*kk) Since -1 < kk < 0, exp(%i*%pi*kk) is complex. Hence, the integral of a real-valued function is complex. That's wrong. This integral uses rectzto%pi2 to evaluate it, which is a rectangle of height 2*%pi. The algorithm seems correct, but the result is clearly wrong. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&group_id=4933 ```
 [Maxima-bugs] [ maxima-Bugs-1451351 ] integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong From: SourceForge.net - 2006-03-28 04:57:19 ```Bugs item #1451351, was opened at 2006-03-16 10:11 Message generated for change (Comment added) made by rtoy You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&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: None Group: None >Status: Closed >Resolution: Fixed Priority: 5 Submitted By: Raymond Toy (rtoy) Assigned to: Nobody/Anonymous (nobody) Summary: integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong Initial Comment: assume(kk<0,kk+1>0); integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf); Answer kk is not an integer. If you exponentialize and factor the result of the integral you get -(log(3)^2+%pi^2)/2*exp(log(3)*kk+%i*%pi*kk) Since -1 < kk < 0, exp(%i*%pi*kk) is complex. Hence, the integral of a real-valued function is complex. That's wrong. This integral uses rectzto%pi2 to evaluate it, which is a rectangle of height 2*%pi. The algorithm seems correct, but the result is clearly wrong. ---------------------------------------------------------------------- >Comment By: Raymond Toy (rtoy) Date: 2006-03-27 23:57 Message: Logged In: YES user_id=28849 This should be fixed in CVS. rectzto%pi2 no longer succeeds on this integral because the exponential part is not a rational function of exp(x). The code has been enhanced to convert this integral to another form using the substitution x=log(y), which results in an integral that maxima knows how to handle. Closing this bug. ---------------------------------------------------------------------- You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=1451351&group_id=4933 ```