Question Number 166702 by metamorfose last updated on 25/Feb/22
$$\int{e}^{{x}} {ln}\left({x}\right){dx}=..??? \\ $$
Commented by mkam last updated on 25/Feb/22
$${u}\:=\:{lnx}\:\rightarrow\:{du}\:=\:\frac{{dx}}{{x}}\:\:,\:{dv}\:=\:{e}^{{x}} \:\Rightarrow\:{v}\:=\:{e}^{{x}} \\ $$$$ \\ $$$${I}=\:{e}^{{x}} {lnx}\:−\:\int\:\frac{{e}^{{x}} }{{x}}\:{dx}\:\:=\:{e}^{{x}} {lnx}\:−\:{Ei}\left({x}\right)\:+\:{C}\: \\ $$