Problem: Let $a\in \mathbb{R}$ Evaluate $\displaystyle \int_0^\infty \dfrac{dx}{(x^4+2ax^2+1)^m} $
Approach: I want to use contour integration to evaluate the desired integral. I tend to choose the close contour is the circle centered at the origin and the radius is $R$. When I solve the roots for $z^4+2az^2+1=0$, I can find the solution, but I cannot determine whether they are in the close contour or not. So I thought this method may fail.