How do I prove convergence of $$\int \_0^1\:\frac{\ln\left(1-x\right)}{\left(1+x\right)^2}dx$$ and if it's convergent, calculate the value of the integral?

I noticed that the values that the function under the integral takes will not be positive on the integration domain $(0,1)$, so I cannot use the convergence criterion with limits.

I tried proving absolute convergence but $\left|\ln\left(1-x\right)\right|\rightarrow \infty $ when $x\rightarrow 1$, so I can't use the comparison criterion either. I'm left with Abel's criterion but I've no idea how to use that, or if it will do me any good.