Primitive of x over x cubed plus a cubed

Theorem

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