\int_{0}^{+\infty}\dfrac{2x u^2(2+u^2)}{(1+a+u^2)(1+x^2u^2)(1+u^2)}du

Uh oh! Wolfram|Alpha doesn't run without JavaScript.

Please enable JavaScript. If you don't know how, you can find instructionshere.Once you've done that, refresh this page to start using Wolfram|Alpha.