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From: Hal Clark <hdeanclark@gm...>  20140823 01:02:36

Hello list, Maxima 5.33.05 is integrating (1/sqrt(c*c + x*x)) dx incorrectly. Entering integrate(1/sqrt(c*c+x*x),x); causes Maxima to spit out asinh(x/abs(c)) which is equal to log((x/abs(c)) + sqrt((x*x/(c*c)) + 1)). The correct result is log(x + sqrt(c*c + x*x)). which I verified with Wolfram Alpha, byhand, and numerically for a few values. So there is a missing factor of c within the log Maxima spits out.  My machine is an x86_64 running an uptodate Arch Linux with sbcl 1.2.2. I'm interacting with Maxima through wxMaxima 13.04.22. $ uname a Linux  3.16.02ARCH #1 SMP PREEMPT Mon Aug 4 19:04:45 CEST 2014 x86_64 GNU/Linux hal 
From: SourceForge.net <noreply@so...>  20110301 12:21:36

Bugs item #3196107, was opened at 20110301 15:21 Message generated for change (Tracker Item Submitted) made by zubkovam You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3196107&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 Private: No Submitted By: andrey zubkov (zubkovam) Assigned to: Nobody/Anonymous (nobody) Summary: Integration bug Initial Comment: Integrals of some positive functions are computed as 0. An example: integrate(x^2*exp(x)/(1+exp(x))^2,x,inf,inf)  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3196107&group_id=4933 
From: SourceForge.net <noreply@so...>  20110302 11:06:37

Bugs item #3196107, was opened at 20110301 07:21 Message generated for change (Comment added) made by dgildea You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3196107&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: Works For Me Priority: 5 Private: No Submitted By: andrey zubkov (zubkovam) Assigned to: Nobody/Anonymous (nobody) Summary: Integration bug Initial Comment: Integrals of some positive functions are computed as 0. An example: integrate(x^2*exp(x)/(1+exp(x))^2,x,inf,inf)  >Comment By: Dan Gildea (dgildea) Date: 20110302 06:06 Message: works in current cvs version. duplicate of bug ID: 3158526.  Comment By: andrey zubkov (zubkovam) Date: 20110301 07:28 Message: Analogous example was posted on 20110115  You can respond by visiting: https://sourceforge.net/tracker/?func=detail&atid=104933&aid=3196107&group_id=4933 
From: Viktor T. Toth <vttoth@vt...>  20140823 05:37:17

The expressions log(x + sqrt(c^2 + x^2)) vs. asinh(x/abs(c)) = log(x/abs(c) + sqrt(1 + (x/c)^2)) differ only by the additive constant log(abs(c)), which can be absorbed into an integration constant. So both are valid forms for the indefinite integral I believe. You can also verify this by differentiating both expressions, and noting that after simplification/factorization, you get back your original expression. Viktor Toth Original Message From: Hal Clark [mailto:hdeanclark@...] Sent: Friday, August 22, 2014 9:02 PM To: maximabugs@... Subject: [Maximabugs] Integration bug Hello list, Maxima 5.33.05 is integrating (1/sqrt(c*c + x*x)) dx incorrectly. Entering integrate(1/sqrt(c*c+x*x),x); causes Maxima to spit out asinh(x/abs(c)) which is equal to log((x/abs(c)) + sqrt((x*x/(c*c)) + 1)). The correct result is log(x + sqrt(c*c + x*x)). which I verified with Wolfram Alpha, byhand, and numerically for a few values. So there is a missing factor of c within the log Maxima spits out.  My machine is an x86_64 running an uptodate Arch Linux with sbcl 1.2.2. I'm interacting with Maxima through wxMaxima 13.04.22. $ uname a Linux  3.16.02ARCH #1 SMP PREEMPT Mon Aug 4 19:04:45 CEST 2014 x86_64 GNU/Linux hal   Slashdot TV. Video for Nerds. Stuff that matters. http://tv.slashdot.org/ _______________________________________________ Maximabugs mailing list Maximabugs@... https://lists.sourceforge.net/lists/listinfo/maximabugs 
From: Hal Clark <hdeanclark@gm...>  20140823 05:41:46

On 8/22/14, Viktor T. Toth <vttoth@...> wrote: > The expressions > > log(x + sqrt(c^2 + x^2)) > > vs. > > asinh(x/abs(c)) = log(x/abs(c) + sqrt(1 + (x/c)^2)) > > differ only by the additive constant log(abs(c)), which can be absorbed > into > an integration constant. So both are valid forms for the indefinite > integral > I believe. You can also verify this by differentiating both expressions, > and > noting that after simplification/factorization, you get back your original > expression. > > > Viktor Toth > Oh  you're right. My mistake. I misdifferentiated when I checked. My numerical comparisons were off by ... log(c). Still, I find it a little surprising that asinh(x/c) is output in lieu of log(x + sqrt(c^2 + x^2)). This is no bug though! Thanks, hal 
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