I need help with the integral.
\begin{equation} I_{n,m}(a,b)=\int dx \frac{x^n \ln(a x^2+b x)}{(a x^2+b x)^m}\,,\enspace\enspace \begin{array}{rcl}n,m &=& {1,2,3,\ldots},\enspace (n\geq m)\\ a, b&\neq&0 \end{array} \end{equation}
I would like to get a result that is some kind of terminating series involving a polynomial of $x$ and their logarithms.
I started by splitting the logarithm and factoring out an $x$ from the denominator:
\begin{equation} I_{n,m}(a,b) = \int dx \frac{x^{n-m}\ln(x)}{(a x+b)^m} + \int dx \frac{x^{n-m}\ln(a x+ b)}{(a x+b)^m} \end{equation}
But, now I'm stuck. I don't know how to calculate either of these integrals.