# [Maxima] Bug in changevar. Should I submit the bug report?

Robert Marik marik at mendelu.cz
Thu Mar 22 09:30:26 CDT 2012

```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.

I was not able to find related bugreport. Should I open new one?
Can you confirm
that this is a new bug? Thanks.

Robert Marik

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Maxima 5.26.0 http://maxima.sourceforge.net
using Lisp SBCL 1.0.50.0.debian
Dedicated to the memory of William Schelter.
The function bug_report() provides bug reporting information.
(%i1) display2d:false;

(%o1) false
(%i2)
changevar('integrate(((cos(x)+sin(x)))^(6)*
(-sin(x)+cos(x)),x),t=cos(x)+sin(x),t,x);

(%o2) 'integrate(sin(x)^6+(6*cos(x)-12*t)*sin(x)^5
+(15*cos(x)^2-60*t*cos(x)+60*t^2)*sin(x)^4
+(20*cos(x)^3-120*t*cos(x)^2+240*t^2*cos(x)-160*t^3)
*sin(x)^3
+(15*cos(x)^4-120*t*cos(x)^3+360*t^2*cos(x)^2
-480*t^3*cos(x)+240*t^4)
*sin(x)^2
+(6*cos(x)^5-60*t*cos(x)^4+240*t^2*cos(x)^3
-480*t^3*cos(x)^2+480*t^4*cos(x)-192*t^5)
*sin(x)+cos(x)^6-12*t*cos(x)^5+60*t^2*cos(x)^4
-160*t^3*cos(x)^3+240*t^4*cos(x)^2-192*t^5*cos(x)
+64*t^6,t)

(%i3) changevar('integrate(cos(x)^6*sin(x),x),t=cos(x),t,x);

solve: using arc-trig functions to get a solution.
Some solutions will be lost.
(%o3) -'integrate(t^6,t)
(%i4) bug_report();

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Maxima version: 5.26.0
Maxima build date: 15:14 3/22/2012
Host type: i686-pc-linux-gnu
Lisp implementation type: SBCL
Lisp implementation version: 1.0.50.0.debian

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The above information is also reported by the function 'build_info'.

(%o4) ""

```