If the value of the integral ${\int }_{-1}^{1}\frac{\cos \alpha x}{1+{3}^{x}}dx$ is $\frac{2}{\pi }$. Then, a value of $\alpha$ is [JEE Main 2024, 4 Apr (Shift 2)]

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If the value of the integral \({\int }_{-1}^{1}\frac{\cos \alpha x}{1+{3}^{x}}dx\) is \(\frac{2}{\pi }\). Then, a value …

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