The discussion centers on whether the integral of e^(x^2) can be expressed in terms of elementary functions. While e^(x^2) is a continuous function and has an anti-derivative, it is not an elementary function. The anti-derivative of e^(x^2) cannot be expressed using standard functions like polynomials or exponentials. The Error Function, erf(x), is mentioned as an anti-derivative for e^(-x^2), but it does not directly apply to e^(x^2). Thus, while e^(x^2) has an integral, it does not have a simple expression in terms of elementary functions.