I asked WolframAlpha to solve a certain differential equation and it gave it in this form: $f(x)=(x-1)(\ln(x-1)-i\pi-1)$. Now I am only interested in this function when $x$ is in the interval $(0,1)$. In this case, I think $f(x)$ will always be a real number.
My question is, is there a way to simplify this expression in the interval $(0,1)$, so that it makes no reference to complex logarithms or imaginary numbers? I just want to express it in terms of real functions.