Let $\int_\alpha^{\log _e 4} \frac{ d x}{\sqrt{ e ^x-1}}=\frac{\pi}{6}$. Then $e ^\alpha$ and $e ^{-\alpha}$ are the roots of the equation: [JEE Main 2024, 8 Apr (Shift 2)]

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Let \(\int_\alpha^{\log _e 4} \frac{ d x}{\sqrt{ e ^x-1}}=\frac{\pi}{6}\). Then \(e ^\alpha\) and \(e ^{-\alpha}\) are t…

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