The value of ${\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{{\cos }^{2}x}{1+{3}^{x}}dx$ is: [JEE Main 2021, 26 Feb (Shift 1)]

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The value of \({\int }_{\frac{-\pi }{2}}^{\frac{\pi }{2}}\frac{{\cos }^{2}x}{1+{3}^{x}}dx\) is: [JEE Main 2021, 26 Feb (…