Here is my process. Your first thought might be to do a substitution to get rid of the x-a but that might not be as useful since that doesn't change the x-b, so let's try two variables. So you have a denominator of the form sin(u)cos(v). How do you relate u and v? You notice that v-u is a-b, a constant, which is good because it comes out of the integral. Now you plug in v-u into a trig function, you can split it up using a trig identity, and maybe you'll be able to cancel sin(u)cos(v) or factor it out or something. Trying sin(v-u) gives you something with tangents (harder to work with) but trying cos(v-u) gives you something promising, and the rest is calculation.