Primitive of Reciprocal of Power of x by Power of Power of x minus Power of a

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^m \ \left({x^n - a^n}\right)^r} = \frac 1 {a^n} \int \frac {\mathrm d x} {x^{m - n} \left({x^n - a^n}\right)^r} - \frac 1 {a^n} \int \frac {\mathrm d x} {x^m \left({x^n - a^n}\right)^{r - 1} }$