Primitive of Reciprocal of x squared plus a squared squared

Theorem

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

Proof
Let: