"integrate" with simple expression takes forever

>>>>> "David" == David Scherfgen <d.scherfgen at googlemail.com> writes:

    David> Hi, it's me again ...
    David> if you calculate this:

    David> integrate(x^(1/3)/(x^(2/3)+1), x, 0, 8);

    David> Maxima will compute forever and never return.
    David> However, the indefinite integral works:

    David> integrate(x^(1/3)/(x^(2/3)+1), x);

    David> gives you the antiderivative:
    David> F(x) := (3*(x^(2/3)+1))/2-(3*log(x^(2/3)+1))/2;

    David> Now I can manually compute my original definite integral as F(8) - F(0).
    David> This is OK, because F(x) doesn't change sign or shows any other
    David> notable behavior between 0 and 8.
    David> The question is: why doesn't Maxima do this? Instead it loops forever ...

Definite integration in maxima uses other algorithms most of the
time.  However, in this case, it does compute the indefinite integral
correctly.  It seems to be stuck computing the limit at 0.  Don't know
why that should present any problem at all.  Maxima easily computes
the limit itself but doesn't seem capable within the integration
routine.

    David> - David

    David> PS: I'm a bit surprised how many bugs Maxima still seems to have, even
    David> though it is so old ...

Because finding bugs is easier than fixing them?  You can help fix the
bugs. :-)

Ray