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.
Dieter Kaiser