Can anybody help me with the values of the following integrals
$\int\limits_0^{2 \pi} (A+\cos(x))^c (A-\cos(x))^{-c} d x$
and more general this integral
$\int\limits_0^{2 \pi} (A+\cos(x))^c (A-\cos(x))^{-c} |\sin(x)|^s d x.$
Here $A \geq 0$, $c$ non-negative, and $s$ complex. A reference to a table with integrals will also be okay.
Thanks.