Primitive of Reciprocal of a x squared plus b x plus c/Zero Discriminant

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

Let $b^2 - 4 a c = 0$.

Then:


 * $\displaystyle \int \frac {\mathrm d x} {a x^2 + b x + c} = \frac {-2} {2 a x + b} + C$

Proof
First:

Put: $z = 2 a x + b$

Let $b^2 - 4 a c = 0$.

Then: