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

Theorem

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