Primitive of x over a x + b/Proof 1

Theorem

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

Proof
Put $u = a x + b$

Then:

Then: