1.
f(x)=∫0xg(t)log⁡e(1−t1+t)dtf(x)=\int_0^x g(t)\log_e(\frac{1-t}{1+t})dt, gg continuous odd. If ∫−π/2π/2(f(x)+x2cos⁡x1+ex)dx=(πα)2−α\int_{-\pi/2}^{\pi/2}(f(x)+\frac{x^2\cos x}{1+e^x})dx = (\frac{\pi}{\alpha})^2-\alpha, then α\alpha is
Integral Calculus - Medium - Question