Primitive of Reciprocal of x cubed by a x + b/Proof 2

Theorem

 * $\displaystyle \int \frac {\mathrm d x} {x^3 \left({a x + b}\right)} = \frac {2 a x - b} {2 b^2 x^2} + \frac {a^2} {b^3} \ln \left\vert{\frac x {a x + b} }\right\vert + C$