\( \int_0^{\infty} \frac{d x}{\left(x^2+a^2\right)\left(x^2+b^2\right)} \text { is }\)

\(\frac{\pi \mathrm{ab}}{\mathrm{a}+\mathrm{b}}\)

\(\frac{\pi }{2(\mathrm{a}+\mathrm{b})}\)

\(\frac{\pi }{2\mathrm{ab}(\mathrm{a}+\mathrm{b})}\)

\(\frac{\pi(a+b)}{2 a b}\)