Question

The value of \( \int_0^\infty \frac{dx}{(x^2 + a^2)(x^2 + b^2)} \) is:

• A. \( \frac{\pi ab}{a + b} \)
• B. \( \frac{ab}{2(a + b)} \)
• C. \( \frac{\pi ab}{a + b} \)
• D. \( \frac{\pi (a + b)}{2ab} \)

Hint:

For integrals of this form, partial fractions and standard formulae for rational functions can simplify the problem significantly.