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Possible Duplicate:
How do you integrate $e^{x^2}$?

When I try to integrate (indefinite) $e^{x^2}$, supposing $x^2 = t$, and integrating by parts, the solutions seem to be never-ending. Is there any other way to integrate this?

Community
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cipher
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2 Answers2

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You can use maclaurin series of $e^{x^2}$ to integrate

Idonknow
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No. It is well-known that there is no elementary antiderivative for $e^{x^2}$.

Gerry Myerson
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  • can i know why? And a glimpse of how can it be done in 'advanced' way? – cipher Jan 20 '13 at 09:53
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    By "elementary", we mean "elementary functions", such as taking powers and multiplying and addition. There is no expression for the integral $e^{x^2}$. We can only give it a name (specfically the "error function"). I don't know how one can prove this. – akkkk Jan 20 '13 at 10:07
  • @akkkk: The error function is related to the integral of $e^{-x^2}$, not $e^{x^2}$. – Mårten W Jan 20 '13 at 21:06
  • @MårtenW: I must admit I missed that, but of course this can be solved by some appropriate complex substitution. – akkkk Jan 20 '13 at 21:52