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The question is $ \displaystyle \int{ \frac{1-r^{2}}{1-2r\cos(\theta)+r^{2}}} d\theta$.

I know it will be used weierstrass substitution to solve but i did not have any idea of it.

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    @GerryMyerson: i am sorry, my mistake.. it is actually involving weierstrass substitution..2011-10-18

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Apply the substitution $\tan \frac{\theta}{2}=t.$ Then use $\cos\theta=\frac{1-t^2}{1+t^2}$.

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    tqsm.. really appreciated.2011-10-18
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There's a Wikipedia article about this technique: Weierstrass substitution.

Notice that what you've got here is $\displaystyle\int\frac{d\theta}{a+b\cos\theta}$. The factor $1-r^2$ pulls out, and $a=1+r^2$ and $b=-2r$.

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    the problems occurs when I try to factorize the denominator in order to use integration by partial fraction. do you have any idea?2011-10-18