Integral of $e^{x^2}$

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What is the integral of $e^{x^2}$? Although I am only a beginner in calculus, all I could understand from a Google search was this resembles a error function (no minus behind the x) and these don't have a simple solution. On the list of integrals of exponential functions on wikipedia,the integral is given, but I cannot understand the result and no further reference or proof is given.