Question Number 30008 by Jmasanja last updated on 14/Feb/18
$${integrate}\:{w}.{r}.{t}\:{x} \\ $$$$\int\left({e}^{{x}^{\mathrm{2}} } \right){dx} \\ $$
Commented by abdo imad last updated on 14/Feb/18
$${we}\:{have}\:{e}^{{u}} \:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{u}^{{n}} }{{n}!}\:\Rightarrow\:{e}^{{x}^{\mathrm{2}} } =\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\frac{{x}^{\mathrm{2}{n}} }{{n}!}\:{and}\:{due}\:{to} \\ $$$${uniform}\:{convergence}\:\:\int\:{e}^{{x}^{\mathrm{2}} } \:{dx}\:=\sum_{{n}=\mathrm{0}} ^{\infty} \:\:\:\frac{{x}^{\mathrm{2}{n}+\mathrm{1}} }{\left(\mathrm{2}{n}+\mathrm{1}\right)\left({n}!\right)}\:\:…. \\ $$