Primitive of x over x cubed plus a cubed

Theorem

 * $\ds \int \frac {x \rd x} {x^3 + a^3} = \frac 1 {6 a} \map \ln {\frac {x^2 - a x + a^2} {\paren {x + a}^2} } + \frac 1 {a \sqrt 3} \arctan \frac {2 x - a} {a \sqrt 3}$