\(\text{ If }{\int }_{-\pi /2}^{\pi /2}\frac{96\left({x}^{2}+\cos x\right)}{1+{e}^{x}}dx=\alpha {\pi }^{3}+\beta \text{ …

\(\text{ If }{\int }_{-\pi /2}^{\pi /2}\frac{96\left({x}^{2}+\cos x\right)}{1+{e}^{x}}dx=\alpha {\pi }^{3}+\beta \text{ (where }\alpha ,\beta \text{ are positive integers),}\\ \text{then }\alpha +\beta \text{ equal to }\) (28 Jan, Shift I, Memory Based)