# What is the antiderivative of e^(x^2)?

It can be written $\frac{2}{\sqrt{\pi}} \text{erfi} \left(x\right)$. Where $\text{erfi} \left(x\right)$ is called the imaginary error function at $x$
The function ${e}^{{x}^{2}}$ has an antiderivative, but there is no nice way to express it using elementary function.
Saying that the antiderivative of ${e}^{{x}^{2}}$ is $\frac{2}{\sqrt{\pi}}$ times the imaginary error function at $x$ doesn't help the intro student much, but that's what it is.