I have an integral:
$\int_{0}^{\frac{1}{B_{1}}}\frac{dx}{x}\ln(x-1)+\int_{0}^{\frac{1}{B_{2}}}\frac{dx}{x}\ln(x-1)$
where
$1<\frac{1}{B_{1}}\leq2 , 2\leq\frac{1}{B_{2}}$
I need to find some finite result. The result should look like ~$(\ln\frac{B_{1}}{B_{2}}+i\pi)^{2}$ or something like that. I am not really sure. Please help. I am stuck with this for a really long time (weeks). Need some hints of complex analysis I think... B1 and B2 are dependent on each other: $B_{12}=\frac{1\pm\sqrt{1-4\tau}}{2}$ , where $0<\tau<1/4$ . There must be the way to get a beautiful and finte answer.