Question Number 107433 by Adilali last updated on 10/Aug/20
$$\int{x}^{{x}} {dx}=? \\ $$
Answered by Dwaipayan Shikari last updated on 10/Aug/20
$$\int{e}^{{xlogx}} {dx} \\ $$$$\int{e}^{{t}} \left(\mathrm{1}+{logx}\right).\frac{\mathrm{1}}{\left(\mathrm{1}+{logx}\right)}{dx}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{xlogx}={t}\:\:,\:\:\mathrm{1}+{logx}=\frac{{dt}}{{dx}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{logxe}^{{logx}} ={t}\:,\:{logx}={W}\left({t}\right) \\ $$$$\int\frac{{e}^{{t}} }{\mathrm{1}+{logx}}{dt}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\int\frac{{e}^{{t}} }{\mathrm{1}+{W}\left({t}\right)}{dt}….. \\ $$