Primitive of Reciprocal of a x squared plus b x plus c/c equal to 0/Proof 1

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

Let $c = 0$.

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

Proof
First: