Question Number 20905 by NECx last updated on 07/Sep/17
$$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$
Commented by NECx last updated on 07/Sep/17
$${please}\:{help} \\ $$
Answered by alex041103 last updated on 07/Sep/17
$${This}\:{integral}\:{cannot}\:{be}\:{expressed}\: \\ $$$${in}\:{elementary}\:{functions} \\ $$$${But}\:{there}\:{is}\:{a}\:{function}\:{defined}\:{using} \\ $$$${this}\:{integral}\:{and}\:{it}\:{is} \\ $$$$\int{e}^{{x}^{\mathrm{2}} } {dx}\:=\:\frac{\sqrt{\pi}}{\mathrm{2}}{erfi}\left({x}\right)\:+\:{C} \\ $$$${For}\:{the}\:{integral}\:\int{e}^{−{x}^{\mathrm{2}} } {dx}\:\left({called}\:\right. \\ $$$$\left.{gaussian}\right)\:{there}\:{is}\:{another}\:{function} \\ $$$$\int{e}^{−{x}^{\mathrm{2}} } {dx}\:=\:\frac{\sqrt{\pi}}{\mathrm{2}}\:{erf}\left({x}\right)\:+\:{C} \\ $$$${Where}\:{erf}\left({x}\right)\:{is}\:{called}\:{the}\: \\ $$$${error}\:{function}. \\ $$
Commented by NECx last updated on 08/Sep/17
$$\mathrm{thanks}\:\mathrm{bro}…..\:\mathrm{mr}\:\mathrm{Alex}\:\mathrm{its}\:\mathrm{been} \\ $$$$\mathrm{a}\:\mathrm{while}\:\mathrm{since}\:\mathrm{i}\:\mathrm{saw}\:\mathrm{your}\: \\ $$$$\mathrm{contribution}\:\mathrm{to}\:\mathrm{questions}…. \\ $$$$\mathrm{feels}\:\mathrm{good}\:\mathrm{to}\:\mathrm{have}\:\mathrm{you}\:\mathrm{back}. \\ $$
Commented by alex041103 last updated on 08/Sep/17
$${Thank}\:{you} \\ $$