# Need help with this definite integral

• I
I'm having a tough time with this integral:

$$\int_{0}^\infty \frac{x^2 \, dx}{x^4+(a^2+\frac{1}{b^2})x^2+\frac{2a^2}{b^2}}$$
where $$a, b \in \Bbb R^+$$ I tried using the residue theorem, but the roots of the denominator I found are quite complicated, and I got stuck.

What contour should I use? Is there an alternative method? I would appreciate any advice.

For partial fractions, the denominator terms will be in terms of $x^2\ not\ x$.