Integral of $$$e^{y^{2}}$$$

Find $$$\int e^{y^{2}}\, dy$$$.

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

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

Therefore,

$$\int{e^{y^{2}} d y} = \frac{\sqrt{\pi} \operatorname{erfi}{\left(y \right)}}{2}$$

Add the constant of integration:

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

$$$\int e^{y^{2}}\, dy = \frac{\sqrt{\pi} \operatorname{erfi}{\left(y \right)}}{2} + C$$$A