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

## 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

- 1968: Murray R. Spiegel:
*Mathematical Handbook of Formulas and Tables*... (previous) ... (next): $\S 15$: Definite Integrals involving Rational or Irrational expressions: $15.20$