I'm having a tough time with this integral:(adsbygoogle = window.adsbygoogle || []).push({});

$$\int_{0}^\infty \frac{x^2 \, dx}{x^4+(a^2+\frac{1}{b^2})x^2+\frac{2a^2}{b^2}}$$

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.

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# I Need help with this definite integral

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