Bugs item #2919396, was opened at 20091222 16:24
Message generated for change (Comment added) made by crategus
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Category: None
Group: None
Status: Open
Resolution: None
Priority: 5
Private: No
Submitted By: Nobody/Anonymous (nobody)
Assigned to: Nobody/Anonymous (nobody)
Summary: improper integral of x*cos(y*x) no longer works
Initial Comment:
I am finding the following possible regression from 5.19.1 to 5.20.0 (also in 5.20.1):
5.19.1
(%i1) integrate(x*cos(y*x),x,minf,inf);
(%o1) 0
5.20.0
(%i1) integrate(x*cos(y*x),x,minf,inf);
(%o1) <ascii art indicating the integral is returned as a nounform>
This is with SBCL and ECL.

>Comment By: Dieter Kaiser (crategus)
Date: 20100111 01:06
Message:
I think this integral should be divergent for all parameters a. Therefore
we have two issues with this integeral:
For an arbitrary parameter a we get a noun form:
(%i1) integrate(x*cos(a*x),x,minf,inf);
(%o1) 'integrate(x*cos(a*x),x,minf,inf)
For a positive parameter we get the result zero:
(%i2) assume(a>0)$
(%i3) integrate(x*cos(a*x),x,minf,inf);
(%o3) 0
(%i4) integrate(x*cos(x),x,minf,inf);
(%o4) 0
Now a negative parameter. Again a noun form:
(%i5) assume(b<0)$
(%i6) integrate(x*cos(b*x),x,minf,inf);
Because we have cos(x) = cos(x) the sign should not change the result. I
think all integrals should be divergent.
Dieter Kaiser

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