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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({x^3 + a^3}\right)} = \frac {-1} {a^3 x} - \frac 1 {6 a^4} \ln \left({\frac {x^2 - a x + a^2} {\left({x + a}\right)^2} }\right) - \frac 1 {a^4 \sqrt 3} \arctan \frac {2 x - a} {a \sqrt 3}$