Any help on this question is
jiskha.com/questions/1788962/Question-Integrate-x-1-sin-a-sin-x-from-0-to-pi-My-first-thought-was-to-apply
(Please add www. to the front as I'm not allowed to post URLs)
I think you're stuck using some kind of numeric or series method. If a is anything other than pi/2 (so the integrand is just x/(1+sinx)) it does not have a solution in elementary functions. Mosey on over to
https://www.wolframalpha.com/input/?i=integral+%5Bx%2F(1%2Bsin+x)%5D+dx
and take a peek. If you change the coefficient of sinx to anything other than 1, you get monstrous complex answers.