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January 12th, 2019, 12:44 AM   #1
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Double integral

How to evaluate this double integral:

$\displaystyle \int_{x=0}^{x=\pi}\int_{y=0}^{y=2\pi}\frac{A^{2}B^ {2}C^{2}\sin x}{\left(A^{2}B^{2}\cos^{2}x+A^{2}C^{2}\sin^{2}x \sin^{2}y+B^{2}C^{2}\sin^{2}x\cos^{2}y\right)^{3/2}}dydx$

where $\displaystyle A,B,C$ are constants.
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January 12th, 2019, 08:04 AM   #2
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The x portion is of the form:

$\displaystyle \int \frac{a\sin x}{(b +c\cos^{2} x)^{\frac{3}{2}}}dx$

Substitute u=cos x and look it up in a table of integrals. The rest should fall into place.
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