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Integration by parts does not seem to work. I was wondering if this integral could be solved using a specific contour and applying for example Jordan's lemma?

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    Now your comment makes sense, I just reread myself for the first time, my double mistake. ;-)2012-03-22

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Elementary functions are generally considered to be functions generated by the identity function, constant functions, basic trig functions, inverse trig functions, exponential functions, logarithmic functions, the four arithmetic operations, and composition. It is well-known that while $\mathrm{e}^{x^2}$ has an antiderivative, that antiderivative is not among the elementary functions.

A name has been given to a similar function $F$, where $F(p)=\frac{2}{\sqrt{\pi}}\int_0^{p}\mathrm{e}^{-x^2}\,dx$. The standard name of this function is the error function, denoted $\operatorname{erf}$. Note the minus sign in the exponent. This explains the name that oenamen gives to your function in his comment.

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    @citrucel: You're welcome.2012-03-21