hard integral 2

dirk_mec1

1. The problem statement, all variables and given/known data

[tex]
\int_0^1 \frac{x^4(1-x)^4}{1+x^2}\ dx
[/tex]

3. The attempt at a solution
A gonio substitution gets nasty really fast moreover the differentiation under the integral sign trick doesn't seem to give more insight (at least that's what I think). Integration by parts gets a ln(.) times something nasty. The boundaries suggest a series expansion or a smart substitution...

Can someone give me a hint?

transgalactic

divide the two polinomials
and youll get an easier integral