Primitive of Reciprocal of Power of x by x cubed plus a cubed

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^n \left({x^3 + a^3}\right)} = \frac {-1} {a^3 \left({n - 1}\right) x^{n - 1} } - \frac 1 {a^3} \int \frac {\mathrm d x} {x^{n - 3} \left({x^3 + a^3}\right)}$