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Solution of the equation $\int_{\log 2}^{x} \frac{d x}{\sqrt{e^{x} - 1}} = \frac{π}{6}$ are

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x = log 6

x = 2 log 2

x = 3

x = 1/2

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detailed solution

Correct option is B

Putting ex−1=t2, we have exdx=2t dtso ∫log⁡2x dxex−1=∫1ex−1 2tdttt2+1=2∫1ex−1 dtt2+1=2tan−1⁡ex−1−π4Thus the given equation reduces totan−1⁡ex−1−π4=π12⇒ex−1=tan⁡π3=3so ex=4⇒x=2log⁡2

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Solution of the equation ∫log⁡2x dxex−1=π6 are

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Solution of the equation $\int_{\log 2}^{x} \frac{d x}{\sqrt{e^{x} - 1}} = \frac{π}{6}$ are