Let \(f\left(x\right)=\int \frac{\left(2-{x}^{2}\right)\cdot {\mathrm{e}}^{x}}{(\sqrt{1+x})(1-x{)}^{3/2}}\mathrm{d}x\). …

Let \(f\left(x\right)=\int \frac{\left(2-{x}^{2}\right)\cdot {\mathrm{e}}^{x}}{(\sqrt{1+x})(1-x{)}^{3/2}}\mathrm{d}x\). If \(f(0)=0\), then \(f\left(\frac{1}{2}\right)\) is equal to:

[JEE Main 2026, 23 Jan (Shift 2)]