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

Theorem

 * $\displaystyle \int_0^\infty \frac 1 {1 + x^n} \rd x = \frac \pi n \csc \left({\frac \pi n}\right)$

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