1. The problem statement, all variables and given/known data ∫-11 dx/(√(1-x2)(a+bx)) a>b>0 2. Relevant equations f(z0)=(1/2πi)∫f(z)dz/(z-z0) 3. The attempt at a solution I have absolutely no idea what I'm doing. I'm taking Mathematical Methods, and this chapter is making absolutely no sense to me. I understand enough to tell I'm supposed to do contour integration on this with a branch cut on the singularity, but actually doing it is another thing. Also, I have no idea what to do with the second term in the denominator. If you can explain this to me, I would be grateful; and please, try to dumb it down. I can't even figure out how to find residues. The farthest I got was K=∫-11dx/(√(1-x2)(a+bx)) + lim r->∞∫0π reiθidθ/(√(1-r2ei2θ)(a+breiθ)) I stopped there, however, because I'm fairly certain I'm embarking on several hours of barking up the wrong tree.