I am currently working on a mathematical problem in QFT when I came across the integral: $$ I=\int_0^1 dx\ln\bigg(\frac{A}{A-x(1-x)B}\bigg) $$ I have no idea how to do such an integral, or where to even start. I am assuming that it will be a contour integral and I will need a branch cut, but that's it.
More info in the physics part: I am working on using Pauli-Villars regularization of a single loop correction to the $\phi^4$ theory.
I got stuck when I used Feynman reparametrization and then ended up with this integral.