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

Theorem

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