# Substitutions for some trig integrals?

1. Nov 24, 2008

### Peeter

Does anybody know substitutions that can be used for the following integrals:

$$\int (a^2 - b^2 \cos\theta)^{-3/2} d\theta$$
$$\int (a^2 - b^2 \cos\theta)^{-3/2} \sin\theta d\theta$$
$$\int (a^2 - b^2 \cos\theta)^{-3/2} \cos\theta d\theta$$

I also had a look for these in my table of integrals, but didn't see anything appropriate, but am also a bit rusty, and could just be overlooking the obvious.

Last edited: Nov 24, 2008
2. Nov 24, 2008

### Peeter

Funny, how asking the question is enough to see the answer. I see what to do with the second one now, and it gets me halfway to:

$$\int (a^2 - b^2 \cos\theta)^{-3/2} e^{i\theta} d\theta$$

which is actually what I was after for the second two. However, it's still not obvious to me what to do with the first nor third integrals.