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

Theorem

 * $\ds \int_0^\infty \frac 1 {1 + x^n} \rd x = \frac \pi n \map \csc {\frac \pi n}$

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