Primitive of p x + q over Root of a x + b

Theorem

 * $\displaystyle \int \frac {p x + q} {\sqrt{a x + b} } \ \mathrm d x = \frac {2 \left({a p x + 3 a q - 2 b p}\right)} {3 a^2} \sqrt{a x + b}$

Proof
Let:

Then: