Primitive of x squared over a x + b/Proof 1

Theorem

 * $\displaystyle \int \frac {x^2 \ \mathrm d x} {a x + b} = \frac {\left({a x + b}\right)^2} {2 a^3} - \frac {2 b \left({a x + b}\right)} {a^3} + \frac {b^2} {a^3} \ln \left\vert{a x + b}\right\vert + C$

Proof
Put $u = a x + b$.

Then:

Then: