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An Integral With A Square Root In The Denominator

  1. Aug 4, 2013 #1
    How would you integrate it?

    [itex]\int \frac{d \varphi}{\sqrt{1 + \frac{a^2 b^2 \sin^2 \alpha}{(a \sin \varphi + b \sin (\alpha - \varphi))^2}}}[/itex]

    I know that solving it numerically would probably be easier, but I would prefer a closed form solution in this case.
  2. jcsd
  3. Aug 4, 2013 #2
    Try putting it as ^-.5 and also remember that a, b and sin^2(alpha) are all constants with respect to d(phi).
    With that in mind try using partial fractions and/or By parts. Tell if You solve it!

    Also pay attention to the fact that every term in the square root is a perfect square!
  4. Aug 5, 2013 #3


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    It is a little work, but as a first step: asinφ + bsin(α-φ) = csin(φ+β) where c and β are constants depending on a,b, and α.
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