Need some help with solving this integral.....

I have to solve the following integral as part of another bigger expression:
$$
int_{A}^{1}{x over 1 – x},(x – A)^{-varepsilon} ln(x)left{1+2left[ln(x) – {1 + x over x},ln(1 – x)right]right} , mathrm{d}x
$$
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 !.