Question Number 168519 by mokys last updated on 12/Apr/22
$$\int\:{x}^{{x}} \:{dx} \\ $$
Answered by Mathspace last updated on 12/Apr/22
$$\int\:{x}^{{x}} {dx}=\int\:{e}^{{xlnx}} {dx} \\ $$$$=\int\:\Sigma\:\frac{\left({xlnx}\right)^{{n}} }{{n}!}{dx} \\ $$$$=\Sigma\frac{\mathrm{1}}{{n}!}\int\:\:{x}^{{n}} \left({lnx}\right)^{{n}} {dx} \\ $$$${and}\:\int\:{x}^{{n}} \left({lnx}\right)^{{n}} {dx}\:{can}\:{be}\:{found}\:{by} \\ $$$${recurrence}…. \\ $$