Integrating e^x^2: Proof & Explanation

[l-1j-cho]

I went through several threads about the integral of e^x^2
but I could not find anything about the proof why e^x^2 cannot be integrated as an elementry function.
Could you explain why?

 

[micromass]

Check Liouville's theorem. A good reference is "Algorithms for computer science" by Geddes, which explains these things in detail!

 

[Hammie]

I went through several threads about the integral of e^x^2
but I could not find anything about the proof why e^x^2 cannot be integrated as an elementry function.
Could you explain why?

I dunno. Maybe because all of the ordinary methods don't work.. maybe this will help.

http://en.wikipedia.org/wiki/Elementary_function