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Question Number 88429 by M±th+et£s last updated on 10/Apr/20
show that  ∫_(0 ) ^1 ln(x) sin^(−1) (√x) dx= (π/2)(ln(2)−1)
$${show}\:{that} \\ $$$$\int_{\mathrm{0}\:} ^{\mathrm{1}} {ln}\left({x}\right)\:{sin}^{−\mathrm{1}} \sqrt{{x}}\:{dx}=\:\frac{\pi}{\mathrm{2}}\left({ln}\left(\mathrm{2}\right)−\mathrm{1}\right) \\ $$

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