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/