## #883 integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf) seems wrong

closed
nobody
None
5
2006-03-28
2006-03-16
Raymond Toy
No

assume(kk<0,kk+1>0);
integrate(x*exp((kk+1)*x)/(exp(x)+3),x,minf,inf);

Answer kk is not an integer.

If you exponentialize and factor the result of the
integral you get

-(log(3)^2+%pi^2)/2*exp(log(3)*kk+%i*%pi*kk)

Since -1 < kk < 0, exp(%i*%pi*kk) is complex. Hence,
the integral of a real-valued function is complex.
That's wrong.

This integral uses rectzto%pi2 to evaluate it, which is
a rectangle of height 2*%pi. The algorithm seems
correct, but the result is clearly wrong.

## Discussion

• Raymond Toy - 2006-03-28

Logged In: YES
user_id=28849

This should be fixed in CVS. rectzto%pi2 no longer succeeds
on this integral because the exponential part is not a
rational function of exp(x). The code has been enhanced to
convert this integral to another form using the substitution
x=log(y), which results in an integral that maxima knows how
to handle.

Closing this bug.

• Raymond Toy - 2006-03-28
• status: open --> closed