Subject: Bug in changevar. Should I submit the bug report?
From: Robert Marik
Date: Thu, 22 Mar 2012 15:19:50 +0000 (UTC)
Robert Marik <marik <at> mendelu.cz> writes:
>
> Dear all,
>
> I think that the following computation is a bug in changevar. Trying
> substitution cos(x)+sin(x)=t in integral of
> (cos(x)+sin(x))^6*(-sin(x)+cos(x))
> I get a mixture of function in t and x variable, see the output of (%o2).
> The same is in version 5.24. Substutitution in
> (cos(x)+sin(x))^(1/6)*(-sin(x)+cos(x)) gives t^(1/6), as expected.
>
Btw, I have the function changevar2 which behaves better in this problem and can
be used to handle more substitutions than ordinary changevar. Allows
substitutions like sin(x)+cos(x)=t if the integral is in the form
"integral of f(phi(x))*phi'(x)*dx". Could be interesting for teachers. Feel free
to reuse, comment or improve the code from
https://bitbucket.org/robert.marik/maw/changeset/e35563446d06 - it is a first
initial version. Examples are at the end of the file. Solves also the problem
from http://www.ma.utexas.edu/pipermail/maxima/2007/008486.html
Robert Marik