Primitive of Reciprocal of x by x fourth minus a fourth

Theorem

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

Proof
From Primitive of $\dfrac 1 {x \left({x^n - a^n}\right)}$:
 * $\displaystyle \int \frac {\mathrm d x} {x \left({x^n - a^n}\right)} = \frac 1 {n a^n} \ln \left\vert{\frac {x^n - a^n} {x^n} }\right\vert + C$

Setting $n = 4$:

directly.