integrate(sqrt(t^c)/(t*(b*t^c+a)),t) hangs



Am Mittwoch, den 04.08.2010, 16:47 +0200 schrieb Dieter Kaiser:
> I have opened a bug report, because the following integral hangs with
> the current version of Maxima
> 
>    integrate(sqrt(t^c)/(t*(b*t^c+a)),t)
> 
> Unfortunately, we had no direct test of this type of integral.
> Therefore, I have overseen this problem.
> 
> As reported in the bug report the problem seems to be that the
> integrator expects simplifications of the Log function which are
> switched off in the current version, because $LOGEXPAND is set to NIL.
> 
> A quick workaround is to bind $LOGEXPAND to NIL in the routine SININT to
> get the old behavior.
> 
> I try to find the underlying problem, because I think the integrator
> should not depend on wrong simplifications like log(1/x) -> -log(x). E.
> g. now we have
> 
> (%i5) integrate(log(1/x),x);
> (%o5) log(1/x)*x+x
> 
> and not x-x*log(x), which is the integral of -log(x).
> 
> A solution or workaround of this problem should be part of an updated
> release of Maxima 5.22.

It is the risch integrator which expects that $logexpand has the value
TRUE. When we bind $logexpand to T in the routine rischint the problem
vanishes.

I think it is the best to do this change in rischint.

Dieter Kaiser