Primitive of x squared over a x + b cubed

Theorem

 * $\ds \int \frac {x^2 \rd x} {\paren {a x + b}^3} = \frac {2 b} {a^3 \paren {a x + b} } - \frac {b^2} {2 a^3 \paren {a x + b}^2} + \frac 1 {a^3} \ln \size {a x + b} + C$

Proof
Put $u = a x + b$.

Then:

Then: