Question Number 126989 by arash sharifi last updated on 25/Dec/20 | ||
$$\int{e}^{\sqrt{{x}}} {dx} \\ $$ | ||
Answered by bramlexs22 last updated on 26/Dec/20 | ||
$${let}\:\sqrt{{x}}\:=\:{u}\:\Rightarrow{x}\:=\:{u}^{\mathrm{2}} \\ $$$$\:\:\:\:\:\:\:{dx}\:=\:\mathrm{2}{u}\:{du}\: \\ $$$${I}=\:\int\:\mathrm{2}{u}\:{e}^{{u}} \:{du}\:...\left({by}\:{parts}\:\right) \\ $$$${I}\:=\mathrm{2}{ue}^{{u}} −\mathrm{2}{e}^{{u}} \:+\:{c}\: \\ $$$${I}=\mathrm{2}\sqrt{{x}}\:{e}^{\sqrt{{x}}} \:−\mathrm{2}{e}^{\sqrt{{x}}} \:+\:{c}\: \\ $$ | ||