Integral of $$$e^{- t^{2}}$$$

Find $$$\int e^{- t^{2}}\, dt$$$.

This integral (Error Function) does not have a closed form:

$${\color{red}{\int{e^{- t^{2}} d t}}} = {\color{red}{\left(\frac{\sqrt{\pi} \operatorname{erf}{\left(t \right)}}{2}\right)}}$$

Therefore,

$$\int{e^{- t^{2}} d t} = \frac{\sqrt{\pi} \operatorname{erf}{\left(t \right)}}{2}$$

Add the constant of integration:

$$\int{e^{- t^{2}} d t} = \frac{\sqrt{\pi} \operatorname{erf}{\left(t \right)}}{2}+C$$

$$$\int e^{- t^{2}}\, dt = \frac{\sqrt{\pi} \operatorname{erf}{\left(t \right)}}{2} + C$$$A