Definite Integral to Infinity of Reciprocal of 1 plus Power of x/Corollary

Theorem

 * $\displaystyle \int_0^\infty \frac 1 {a^n + x^n} \rd x = \frac \pi {n a^{n - 1} } \csc \paren {\frac \pi n}$

where:
 * $n$ is a real number greater than 1
 * $\csc$ is the cosecant function
 * $a \ne 0$.