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

If \({\int }_{-\frac{\pi }{2}}^{\frac{\pi }{2}}\frac{96{x}^{2}{\cos }^{2}x}{\left(1+{e}^{x}\right)}dx=\pi \left(\alpha {\pi }^{2}+\beta \right),\alpha ,\beta \in Z,\) then \((\alpha +\beta {)}^{2}\) equals

[JEE Main 2025, 28 Jan (Shift 1)]