How to integrate
$$
\int\_0^\alpha 2x\ln|\frac{x-1}{x+1}| dx
$$
where $\alpha>1$.

Attempts:
Integrate by parts, we have
$$
\alpha^2\ln|\frac{\alpha-1}{\alpha+1}|-\int\_0^\alpha \frac{2x^2}{x^2-1} dx
$$
The second part diverges when evaluate by Mathematica.