Primitive of x squared over Root of a x + b

Theorem

 * $\displaystyle \int \frac {x^2 \ \mathrm d x} {\sqrt{a x + b} } = \frac {2 \left({3 a^2 x^2 - 4 a b x + 8 b^2}\right) \sqrt{a x + b} } {15 a^3}$

Proof
Let:

Thus:

Then: