Originally Posted by

**topsquark** These cropped up in one of my calculations. I have forgotten if they are even possible to integrate and I can't find the reference, so I'd appreciate a hand. (I will note that at least one of these looks suspiciously like an elliptic integral.)

$\displaystyle \int_0^{2 \pi} (b - a~cos( \phi - \alpha ) )^{3/2} \left \{ \begin{matrix} 1 \\ sin( \alpha ) \\ cos( \alpha ) \end{matrix} \right \} ~ d \alpha$

We may take b > a > 0 WLOG.

Any help/thoughts would be appreciated.

-Dan