I have to solve the following integral as part of another bigger expression: $$ \int_{A}^{1}{x \over 1 - x}\,(x - A)^{-\varepsilon} \ln(x)\left\{1+2\left[\ln(x) - {1 + x \over x}\,\ln(1 - x)\right]\right\} \, \mathrm{d}x $$ where $\epsilon$ is a small parameter.
- I tried to plug this into ${\tt Mathematica}$ but it doesn't give any solution.
- Then I tried to solve it by hand using the $u$-substitute but it always produces some other integral similar to this one that is complicated to solve.
Is there any smart choice of variable substitute to solve this ?. I would really appreciate any help or insight !.