That can not be done. There is no elementary function whose derivative is [itex]e^{x^2}[/itex]. There is a special function, erf(z) defined by:
[tex]erf(z)=\frac{2}{\sqrt{\pi}} \int_{0}^{z} e^{t^2}dt[/tex]
Is that the full question, or was it a definite integral? There are special tricks to finding certain definite integrals of this function.