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

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({x^4 + a^4}\right)} = \frac {-1} {a^4 x} - \frac {-1} {4 a^5 \sqrt 2} \ln \left({\frac {x^2 - a x \sqrt 2 + a^2} {x^2 + a x \sqrt 2 + a^2} }\right) + \frac 1 {2 a^5 \sqrt 2} \left({\arctan \left({1 - \frac {x \sqrt 2} a}\right) - \arctan \left({1 + \frac {x \sqrt 2} a}\right)}\right)$