Question

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

Answer 1

It is `sqrtpi/2` times a function called the imaginary error function.

Explanation:

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=oo` here

http://www.wolframalpha.com/input/?i=series+int+e%5E(x%5E2)+dx