Primitive of Reciprocal of x squared by x cubed plus a cubed/Lemma

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({x^3 + a^3}\right)} = \frac {-1} {a^3 x} - \frac 1 {a^3} \int \frac {x \ \mathrm d x} {\left({x^3 + a^3}\right)}$