Difficult Integral of trig and sqrt functions

[dm164]

I'm having troubles solving this integral.

∫ (sinx)^2 / √( a - b*cos(x)) dx ; a & b just constants

I've tried many routes but get stuck.
And when substitution and product rule methods seem to fail. Are there other methods useful to go to when integrating strange functions?

 

[LCKurtz]

I'm having troubles solving this integral.

∫ (sinx)^2 / √( a - b*cos(x)) dx ; a & b just constants

I've tried many routes but get stuck.
And when substitution and product rule methods seem to fail. Are there other methods useful to go to when integrating strange functions?

When standard methods fail, which is often for "strange" functions I usually try to see if Maple gives an answer. Maple seems to have a built in solver that knows many of the non-standard and lesser studied integrals. For this example I set a = 4 and b = 2 just to see what would happen and Maple gives an answer in terms of Elliptic functions. You aren't going to solve it with the standard calculus methods.