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

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

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