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Question Number 65827 by ~ À ® @ 237 ~ last updated on 04/Aug/19

Prove that    ∫_0 ^1 (∫_(1/6) ^(5/6)   (dv/((1−^v (√u) )^v )))du=ln2−2ln((√3)−1)

$${Prove}\:{that}\:\: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \left(\int_{\frac{\mathrm{1}}{\mathrm{6}}} ^{\frac{\mathrm{5}}{\mathrm{6}}} \:\:\frac{{dv}}{\left(\mathrm{1}−\:^{{v}} \sqrt{{u}}\:\right)^{{v}} }\right){du}={ln}\mathrm{2}−\mathrm{2}{ln}\left(\sqrt{\mathrm{3}}−\mathrm{1}\right) \\ $$

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