Question Number 142438 by rs4089 last updated on 31/May/21
$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{1}−{x}}{{lnx}}{dx} \\ $$$${how}\:\:{many}\:{tricks}\:{solve}\:{this} \\ $$
Answered by Dwaipayan Shikari last updated on 31/May/21
$${log}\left(\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$
Commented by Dwaipayan Shikari last updated on 31/May/21
$${Generally}\:\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{{a}} −\mathrm{1}}{{log}\left({x}\right)}\:{dx}={log}\left({a}+\mathrm{1}\right)\: \\ $$