integration of e^-x^2

[Pi3.1415]

Hello, I was just wondering if anyone new of a proof that their is no elementary integral for: e^-x^2
Any help would be appreciated. :smile:

[gb7nash]

Hello, I was just wondering if anyone new of a proof that their is no elementary integral for: e^-x^2
Any help would be appreciated. :smile:

Hi Pi,

If you're interested in proving these, it looks like differential galois theory is your best bet. If you just started taking calculus though, you might have to wait a bit to prove it. :redface:

[Pi3.1415]

Hi Pi,

If you're interested in proving these, it looks like differential galois theory is your best bet. If you just started taking calculus though, you might have to wait a bit to prove it. :redface:

Thank you. My knowledge of Galois Theory is weak to put it in a good light, but i don't see how it could be applied in this situation. Could you please help?

[gb7nash]

Thank you. My knowledge of Galois Theory is weak to put it in a good light, but i don't see how it could be applied in this situation. Could you please help?

Unfortunately, my knowledge on galois theory is very limited. There might some other simpler method but I don't know it.

[Pi3.1415]

Okay thank you anyway; I *think* I've found a way using Liouville Theorem (which I've never heard of before).