Definite Integral to Infinity of Power of x over Power of x plus Power of a

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Theorem

$\displaystyle \int_0^\infty \dfrac {x^m \rd x} {x^n + a^n} = \frac {\pi a^{m + 1 - n} } {n \sin \left({\left({m + 1}\right) \frac \pi n}\right)}$

for $0 < m + 1 < n$.


Proof


Sources