Question Number 76048 by peter frank last updated on 22/Dec/19
$$\int{e}^{{x}^{\mathrm{2}} } {dx} \\ $$
Answered by Crabby89p13 last updated on 23/Dec/19
$${Actually}\:{there}\:{is}\:{no}\:{elementary} \\ $$$${function}\:{that}\:{describes}\:{the}\:{integral}\:{of} \\ $$$${e}^{{x}^{\mathrm{2}} } \:{You}\:{can}\:{however}\:{express} \\ $$$${this}\:{Integral}\:{in}\:{terms}\:{of}\:{an} \\ $$$${infinite}\:{series}\:{by}\:{plugging}\:{in}\:{x}^{\mathrm{2}} \\ $$$${into}\:{x} \\ $$$$ \\ $$$${e}^{{x}^{\mathrm{2}} } =\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{{x}^{\mathrm{2}{n}} }{{n}!} \\ $$
Answered by benjo last updated on 23/Dec/19
$${this}\:{is}\:{Gaussian}\:{integral} \\ $$