I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure how.
$$ \int_{0}^{\infty}\int_{0}^{\pi} {r^{4}\sin^{3}\left(\theta\right) \over \left\{(r^{2} + d^{2}/4)^2 - \left[rd\cos\left(\theta\right)\right]^{2}\right\}^{3/2}} \,{\rm d}r\,{\rm d}\theta \space-[1] $$
If I focus on the integration w.r.t. r first, I get [2]. If I focus on the integration w.r.t. $\theta$ first, I get [3]. A,B,C are just constants w.r.t. the variable of integration.
I believe I can make a series of substitutions but they don't seem to get me closer to an answer.
$$ \int_{0}^{\infty} {Ar^{4} \over \left[(r^{2} + B)^2 -\left(rC\right)^{2}\right]^{3/2}}\,{\rm d}r \space-[2] $$
$$ \int_{0}^{\pi} {A\sin^{3}\left(\theta\right) \over \left\{(C)^2 - \left[B\cos\left(\theta\right)\right]^{2}\right\}^{3/2}} \,{\rm \rm d}\theta \space-[3] $$