Calculate this integral $\int \frac{x^2}{4x^4+25}dx$. I have to calculate this integral $\int \frac{x^2}{4x^4+25}dx$.
I dont have any idea about that.
I thought about parts integration.
Thanks.

Hint Apply the factorization
$$a^4 + b^4 = (a^2- \sqrt{2} a b + b^2) (a^2 + \sqrt{2} a b + b^2)$$
to the denominator and apply the Method of Partial Fractions to decompose the integrand.
