Definite Integral from 0 to a of x^m by (a^n - x^n)^p

Theorem

 * $\displaystyle \int_0^a x^m \left({a^n - x^n}\right)^p \rd x = \frac {a^{m + 1 + n p} \, \Gamma \left({\frac {m + 1} n}\right) \Gamma \left({p + 1}\right)} {n \Gamma \left({\frac {m + 1} n + p + 1}\right)}$