Primitive of Reciprocal of x cubed by a x + b squared

Theorem

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