# Re-writing integral of x^x

• Apr 18th 2011, 02:48 AM
strugglingstudent1
Re-writing integral of x^x
Hello and thanks to those reading my question.

I don't know if this can be done, but I'm trying to re-write the integral of x^x in the form of an integral of R(x) e^g(x) where R(x) and g(x) are rational functions.

Starting from x^x = e^(x ln(x)) I have tried various substitutions (eg. u = ln(x), u = e^x etc.) and also integration by parts but have had no luck.

As I said, I'm not sure if what I'm trying to do can be done, but if it can I'm hoping someone can see how to do it and suggest a productive approach.

• Apr 18th 2011, 03:48 AM
FernandoRevilla
The antiderivative of f( x ) = x^x can not be expressed in terms of elementary functions.
• Apr 18th 2011, 06:00 AM
mr fantastic
Quote:

Originally Posted by FernandoRevilla
The antiderivative of f( x ) = x^x can not be expressed in terms of elementary functions.

I think the OP knows that. S/he is asking how to express the integral in terms of another integral, not how to integrate x^x. (Probably wants to use the special case of Liouville's strong theorem to prove what you have stated).
• Apr 18th 2011, 06:36 AM
FernandoRevilla