Let f(x)=∫_0^x g( t ) log_e ((1- t)/(1+ t)) dt, where g is a continuous odd function. If ∫_-π / 2^π / 2(f(x)+(x^2 cos x)/(1+ e^x)) d x=((π)/(α))^2-α,…

Let $\displaystyle f(x)=\int_0^x g(\mathrm{t}) \log _{\mathrm{e}}\left(\frac{1-\mathrm{t}}{1+\mathrm{t}}\right) \mathrm{dt}$, where $\displaystyle g$ is a continuous odd function. If $\displaystyle \int_{-\pi / 2}^{\pi / 2}\left(f(x)+\frac{x^2 \cos x}{1+\mathrm{e}^x}\right) \mathrm{d} x=\left(\frac{\pi}{\alpha}\right)^2-\alpha$, then $\displaystyle \alpha$ is equal to $\displaystyle \_\_\_\_$.