The value of the integral ${\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\left(\frac{32{\cos }^{4}x}{1+{e}^{\sin x}}\right)dx$ is: [JEE Main 2026, 6 Apr (Shift 1)]

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The value of the integral \({\int }_{-\frac{\pi }{4}}^{\frac{\pi }{4}}\left(\frac{32{\cos }^{4}x}{1+{e}^{\sin x}}\right)…

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