Primitive of x squared over Root of a x + b

Theorem

 * $\ds \int \frac {x^2 \rd x} {\sqrt {a x + b} } = \frac {2 \paren {3 a^2 x^2 - 4 a b x + 8 b^2} \sqrt {a x + b} } {15 a^3}$

Proof
Let:

Thus:

Then: