Primitive of x over square of a x squared plus b x plus c

Theorem
Let $a \in \R_{\ne 0}$.

Then:
 * $\displaystyle \int \frac {x \ \mathrm d x} {\left({a x^2 + b x + c}\right)^2} = \frac {- \left({b x + 2 c}\right)} {\left({4 a c - b^2}\right) \left({a x^2 + b x + c}\right)} - \frac b {4 a c - b^2} \int \frac {\mathrm d x} {a x^2 + b x + c}$

Proof
Let:

Then: