Primitive of Reciprocal of x cubed plus a cubed/Lemma

Lemma for Primitive of Reciprocal of $x^3 + a^3$

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

Proof
The discriminant of $x^2 - a x + a^2$ is:

Thus: