[Maxima-bugs] [ maxima-Bugs-2948800 ] integrate((1-cos(2*x)^2)^2/x^4 wrong

[SourceForge.net <no...@so...>]

Bugs item #2948800, was opened at 2010-02-10 01:09
Message generated for change (Tracker Item Submitted) made by crategus
You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2948800&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: Lisp Core - Integration
Group: None
Status: Open
Resolution: None
Priority: 1
Private: No
Submitted By: Dieter Kaiser (crategus)
Assigned to: Nobody/Anonymous (nobody)
Summary: integrate((1-cos(2*x)^2)^2/x^4 wrong

Initial Comment:
We get the following result for the function sin:

(%i7) integrate((sin(2*x)^2)^2/x^4,x,0,inf);
(%o7) 8*%pi/3

But not when we insert the equivalent expression 1-cos(2*x)^2 for sin(2*x)^2:

(%i8) integrate((1-cos(2*x)^2)^2/x^4,x,0,inf);
defint: integral is divergent.
 -- an error. To debug this try: debugmode(true);

It works when we have an argument x without a factor:

(%i9) integrate((sin(x)^2)^2/x^4,x,0,inf);
(%o9) %pi/3

(%i10) integrate((1-cos(x)^2)^2/x^4,x,0,inf);
(%o10) %pi/3

The error is in the routine ssp in the file defint.lisp. This routine does the substitution sin(x)^2 for 1-cos(x)^2. But the function does not look at the complete argument of the trig function. It takes only into account the variable of integration.

Dieter Kaiser

----------------------------------------------------------------------

You can respond by visiting: 
https://sourceforge.net/tracker/?func=detail&atid=104933&aid=2948800&group_id=4933