# What is the integral of $e^{ax^2}$? [closed]

What is the integral of this function:

$$f(x) = e^{ax^2},\quad x>0$$

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## closed as not a real question by Nate Eldredge, Asaf Karagila, Hagen von Eitzen, Davide Giraudo, DidFeb 15 '13 at 16:02

It's difficult to tell what is being asked here. This question is ambiguous, vague, incomplete, overly broad, or rhetorical and cannot be reasonably answered in its current form. For help clarifying this question so that it can be reopened, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

Are you asking for in indefinite integral (there is none representable as elementary functions) or for a definite integral on $[0,\infty)$? What have you tried? I have edited your math into LaTeX format. Edit your question and resolve the issues I pointed out. –  ncmathsadist Feb 15 '13 at 15:02

There is no elementary antiderivative, but with the imaginary errorfunction it is $$\frac{\sqrt{\pi} \operatorname{erfi}(\sqrt{a} x)}{2 \sqrt{a}}$$ For the definite you can use a substitution to polar coordinates to solve it.