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

Find $$$\int e^{- a^{2}}\, da$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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