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

Find $$$\int e^{p^{2}}\, dp$$$.

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

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

Therefore,

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

Add the constant of integration:

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

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