Is there a proof that there is no elementary integral for 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.

 

[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.

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.

 

[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.

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).