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

Theorem

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

Proof
Let: