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

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

Then:
 * $\displaystyle \int \frac {\mathrm d x} {x^2 \left({a x^2 + b x + c}\right)} = \frac b {2 c^2} \ln \left\vert{\frac {a x^2 + b x + c} {x^2} }\right\vert - \frac 1 {c x} + \frac {b^2 - 2 a c} {2 c^2} \int \frac {\mathrm d x} {a x^2 + b x + c}$