Integral of $$$e^{- x^{2}}$$$
The calculator will find the integral/antiderivative of $$$e^{- x^{2}}$$$, with steps shown.
Related calculator: Integral Calculator
Solution
This integral (Error Function) does not have a closed form:
$${\color{red}{\int{e^{- x^{2}} d x}}} = {\color{red}{\left(\frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}\right)}}$$
Therefore,
$$\int{e^{- x^{2}} d x} = \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}$$
Add the constant of integration:
$$\int{e^{- x^{2}} d x} = \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2}+C$$
Answer
$$$\int e^{- x^{2}}\, dx = \frac{\sqrt{\pi} \operatorname{erf}{\left(x \right)}}{2} + C$$$A