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

Theorem

 * $\ds \int_0^\infty \dfrac {x^m \rd x} {x^n + a^n} = \frac {\pi a^{m + 1 - n} } {n \map \sin {\paren {m + 1} \frac \pi n} }$

for $0 < m + 1 < n$.