Subject: "integrate" with simple expression takes forever
From: David Scherfgen
Date: Thu, 08 Nov 2012 16:31:55 +0100
Hi, it's me again ...
if you calculate this:
integrate(x^(1/3)/(x^(2/3)+1), x, 0, 8);
Maxima will compute forever and never return.
However, the indefinite integral works:
integrate(x^(1/3)/(x^(2/3)+1), x);
gives you the antiderivative:
F(x) := (3*(x^(2/3)+1))/2-(3*log(x^(2/3)+1))/2;
Now I can manually compute my original definite integral as F(8) - F(0).
This is OK, because F(x) doesn't change sign or shows any other notable
behavior between 0 and 8.
The question is: why doesn't Maxima do this? Instead it loops forever ...
- David
PS: I'm a bit surprised how many bugs Maxima still seems to have, even
though it is so old ...