Is there a closed form expression for $\int\frac{1}{a-b\ln(cx)}\,\mathrm dx\ ?$
I was wondering how to integrate the above function. I have spent a lot of time on it. First i did an integration by parts until I had to integrate $\ln|a – b \ln(c x)|$ again. Once more, I did an integration by parts and substituted this value back into the original equation. However, now all the terms cancel each other out, effectively giving $0 = 0$. How do I go about integrating $1/(a-b \ln(cx))$? Thanks for the assistance.
Edit: $a$, $b$ and $c$ are constants.