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

### Integral of Exponents, Natural Logs...

```
Date: 8/27/96 at 6:13:40
From: Wim De Blay
Subject: Integral of Exponents, Natural Logs...

Hi guys,

Can you solve this integration?

INT x^(-ln x).e^(-x.lnx + x).dx
```

```
Date: 9/5/96 at 10:3:49
From: Doctor Jerry
Subject: Re: Integral of Exponents, Natural Logs...

I think it is likely that this integral can't be done in finite terms.
I say this since if you make the substitution ln(x) = z, the integral
becomes (using e^w to denote exp(w))

(**)     int(e^(-z^2)*e^(e^z) dz).

Since it is known that the integral int(e^(-z^2) dz) can't be done in
finite terms (it is closely related to the normal probability density
function and to the error function erf), it seems likely to me that
the more complex  integral (**) also can't be done in finite terms.

-Doctor Jerry,  The Math Forum
Check out our web site!  http://mathforum.org/dr.math/
```
Associated Topics:
College Calculus
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