Question

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

Answer 1

It can be written `2/sqrtpi "erfi"(x)`. Where `"erfi"(x)` is called the imaginary error function at `x`

Explanation:

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 `2/sqrtpi` times the imaginary error function at `x` doesn't help the intro student much, but that's what it is.