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

It is $\frac{\sqrt{\pi}}{2}$ times a function called the imaginary error function.
The function ${e}^{{x}^{2}}$ has an antiderivative that is not finitely expressible using elementary function.
You can look up the series expansions at $x = 0$ and at $x = \infty$ here