Closed form $\int_{a}^b \cfrac{1}{(1+x) \, \left[\ln(1-x)-\ln(1+x)\right]} \, \mathrm{d}x$

Question

I am encountering an integral which involves logarithms, in particular,

\begin{equation} \int_{a}^b \cfrac{1}{(1+x) \, \left[\ln(1-x)-\ln(1+x)\right]} \, \mathrm{d}x, \end{equation} where $a$ and $b$ are finite real numbers.

Does this integral have an closed form solution ? It seems that integration by parts does not work...