Primitive of x squared over x squared plus a squared squared/Proof 1

Theorem

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

Proof
Let: