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Question Number 142438 by rs4089 last updated on 31/May/21

∫_0 ^1 ((1−x)/(lnx))dx  how  many tricks solve this

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{{lnx}}{dx} \\ $$$${how}\:\:{many}\:{tricks}\:{solve}\:{this} \\ $$

Answered by Dwaipayan Shikari last updated on 31/May/21

log((1/2))

$${log}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$

Commented by Dwaipayan Shikari last updated on 31/May/21

Generally ∫_0 ^1 ((x^a −1)/(log(x))) dx=log(a+1)

$${Generally}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{a}} −\mathrm{1}}{{log}\left({x}\right)}\:{dx}={log}\left({a}+\mathrm{1}\right)\: \\ $$

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