I'm trying to calculate an integration over an arbitrary polygon $P$, and a point $p$ is on $P$.
$k$ is a constant, and $A(x,y,z)$ and $B(x,y,z)$ are arbitrary functions returning a scalar.
As $\int_P \frac{dp}{A(p)}$ and $\int_P \frac{dp}{B(p)}$ are known, I'd like to solve $\int_P \ln(1+\frac{2k}{A(p)+B(p)-k}) dp$. One of the solutions is to approximate the logarithmic function by expressing it using $\frac{1}{A}$ and $\frac{1}{B}$. I tried to approximate the function by using Taylor series, but I failed.
I sincerely want your kind answers :D