Question

what is the integral of e^(x^2)

Answer 1

It is an Impossible integral, Simply because e^(x^2) is something known as an elementary function when taking the integral. So we define it as such and called it Erf(x) function.

Integral e^(x^2) = 1/2 Sqrt(pi) Erf(x) +C

Answer 2

elouis950 is correct. Browse over to WolframAlpha.com and paste in the following:

Integrate E^(x^2) with respect to x

They will provide you with plots and some related series expansions.