integration - Improper Integral - Partial Fractions or a Trick?

$$\int_{-\infty}^{\infty}\frac{dx}{(x^2+ax+a^2)(x^2+bx+b^2)}$$
a and b are real constants

How should I solve the above integral? Is there a nice, interesting method? or is partial fractions the only way to do it?

I did solve it using partial fractions, but it got really lengthy and cumbersome - wondering if there's a nicer way to do it.

Thanks a lot!