JEE Main 202429 Jan, Morning shiftMathematicsMediumIntegral Calculus369× since 2002
If the value of the integral \int_\limits{-\frac{\pi}{2}}^{\frac{\pi}{2}}\left(\frac{x^2 \cos x}{1+\pi^x}+\frac{1+\sin ^2 x}{1+e^{\sin x^{2123}}}\right) d x=\frac{\pi}{4}(\pi+a)-2, then the value of is