Substitutions for some trig integrals?

[Peeter]

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

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

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.

EDIT: oops. fixed sign in square root.

 

[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:

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

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.