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Substitutions for some trig integrals?

  1. Nov 24, 2008 #1
    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.

    EDIT: oops. fixed sign in square root.
    Last edited: Nov 24, 2008
  2. jcsd
  3. Nov 24, 2008 #2
    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.
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