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

Theorem

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

Proof
Put $u = a x + b$.

Then:

Then: