# Is this elementary.

• January 19th 2006, 01:08 PM
ThePerfectHacker
Is this elementary.
Is $x^x$ an elementary function?
I do not think it is, is that right?
• January 19th 2006, 04:44 PM
Jameson
I think it is elementary. The integral however isn't. Check out MathWorld's page on elementary functions for a definition.

http://mathworld.wolfram.com/ElementaryFunction.html
• January 19th 2006, 05:36 PM
hpe
Quote:

Originally Posted by ThePerfectHacker
Is $x^x$ an elementary function?

$x^x = e^{x \cdot \ln x}$, so it's elementary.
• January 19th 2006, 06:00 PM
ThePerfectHacker
Curious, why is $\int e^{x^2}dx$ not elementary? How do you prove it?

It seems to be anagolus with Galios' Theory for the insolvability of the quintic. Namely, to show that in finite steps a solution cannot be reached.