Associated Topics || Dr. Math Home || Search Dr. Math

### The Integral of e^(x^2)dx

```
Date: 03/26/98 at 10:37:06
From: Manuel Ruiz Martinez
Subject: How should I solve the integral e^(x^2)?

I understood some of the concepts that you wrote about there. I am
Complutense in Madrid, or in Valencia.

And the question, the integral of e^(x^2). I have a program named
Derive. With this program the solution is very strange. I don't know
if you will be able to help me, but I think so.

Manuel
```

```
Date: 03/27/98 at 08:03:54
From: Doctor Jerry
Subject: Re: How should I solve the integral e^(x^2)?

Hi Manuel,

There are many functions - called special functions - which fail to
have an anti-derivative expressible as a finite combination of
elementary functions. The so-called elliptic functions, the error
function, and the gamma function are a few examples. The error
function, which is extremely useful in both physics and statistics, is
defined as:

erf(x) = (2/sqrt(pi))integral from 0 to x of e^(-t^2)dt

This is closely related to the problem you mentioned. Neither can be
done in finite terms.

There would not exist extensive tables of the error function if the
anti-derivative of e^(-t^2) were expressible as a finite combination
of elementary functions.

The Annals can be found in the library of any good university.

-Doctor Jerry,  The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Calculus

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search