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e-x-2-dx-




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

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