Dear Stackexchange users,
I would like to integrate the following function using Mathematica as I don't have a way of doing this by hand:
$$\int_0^\pi \frac{\log(A-B\cos\theta)\sin^4\theta}{(A-B\cos\theta)^2}d\theta$$
Within Mathematica I apply the assumption that $A$ and $B$ are real and that with $A>0, B>0$ and $A>B$. Note that Mathematica will quite happily do the following integration:
$$\int_0^\pi \frac{\log(A-B\cos\theta)\sin^4\theta}{(A-B\cos\theta)}d\theta$$
I can numerically integrate this but I would like an analytic result if possible.
Any help is greatly appreciated.