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

Theorem

 * $\ds \int \frac {\d x} {x^n \paren {x^3 + a^3} } = \frac {-1} {a^3 \paren {n - 1} x^{n - 1} } - \frac 1 {a^3} \int \frac {\d x} {x^{n - 3} \paren {x^3 + a^3} }$