Hi, the integral I'm trying to solve is:(adsbygoogle = window.adsbygoogle || []).push({});

[tex] \int \frac{1}{1+\sin^2{\theta}}d\theta [/tex]

From 0 to pi, which is the same as half the same integral over the unit circle.

I changed the sine squared into 1-cos[2x] and then expressed cos[2x] as half z^2 +(z-1)^2 and i finally got it in this form:

[tex] \frac{1}{i} \int \frac{z}{-z^4+z^2-1} dz [/tex]

I found out the poles to be -1/2 +- i sqrt(3)/2 which happen to be on the countour path, and in that case i don't know how to apply the residue theorem, if it could be applied that is.

Edit: The answer is given in the book to be pi/sqrt(2)

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# Help with an integral, yet again.

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