# Primitive of exp (-x^2) has no Solution in Elementary Functions

## Theorem

The primitive:

$\displaystyle \int \map \exp {-x^2} \rd x$

cannot be expressed in terms of a finite number of elementary functions.

## Historical Note

The proof that $\ds \int \map \exp {-x^2} \rd x$ cannot be expressed with a finite number of elementary functions was first proved by Joseph Liouville.