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I'm supposed to verify that this: $$\int_0^\infty \frac{dx}{x^p(x^2+2x\cos{\phi}+1)}=\pi\frac{\sin{p\phi}}{\sin{p\pi}\sin{\phi}}$$

where $0 and $0<\phi<\pi$

How do I do this with a keyhole contour?

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    Are you sure the limits of integration are $0$ to $+\infty$ and not $-\infty$ to $+\infty$?2012-12-08
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    I'm sure they're right.2012-12-08
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    Have a look at (for example): http://math.stackexchange.com/questions/114884/is-there-an-elementary-method-for-evaluating-int-0-infty-fracdxxs-x1 and see if you can't do it yourself afterwards. Writing a complete answer to these kinds of questions is *a lot* of work.2012-12-08

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