I'm having trouble with the following integral
$\int_0^{\infty} {x^2 \over (x^2+A)^n} \ dx \ \ \text{for} \ \ A \gt 0 $
EDIT:
I had previously thought that the answer to the integral above was:
$ {2\over(n-1)(n-2)(n-3)A^{n-3}}$
But actually this is the answer to:
$\int_0^{\infty} {x^5 \over (x^2+A)^n} \ dx \ \ \text{for} \ \ A \gt 0 $
which is much easier to integrate (this is one book misprint I'll never forget). BD answer below made me see that (he tested it numerically).
Still, since I spent 4 days trying to solve the wrong integral, it is a relief to see a answer to that and to see how complicated it is. This is a sneaky integral right there, seems to be easy until you get down to business. Too bad I have to choose one answer, there are many good ones.