If f(x) = ∫ g(t)ln(1−t/1+t) dt; t ∈ [0, x] and g is odd continuous function and

Question

If \(f(x) = \int \limits_0^x g(t) \ln \left(\frac{1-t}{1+t} \right) dt \) and g is odd continuous function and \(\int\limits_{-\frac \pi 2}^{\frac \pi 2} \left(f(x) + \frac{x^2\cos x}{(1+e^x)} \right)dx = \frac{\pi ^2}{\alpha ^2} - \alpha\) then α is _____.

Answer 1

\(\therefore f(x) = \int \limits_0^x g(t) \ln \left(\frac{1-t}{1+t} \right) dt \)