\int\frac{1}{x^m\left(a+bx\right)^p}dx\quad\to\quad\frac{1}{\left(\left(p-1\right)a\right)x^{m-1}\left(a+bx\right)^{p-1}}+\frac{m+p-2}{\left(p-1\right)a}\int\frac{dx}{x^m\left(a+bx\right)^{p-1}}