Integrating Hard Integral 2: Can Someone Give Me a Hint?

[dirk_mec1]

Homework Statement

$$\int_0^1 \frac{x^4(1-x)^4}{1+x^2}\ dx$$

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