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?
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?