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\begin{align}
{\rm E}\pars{x^{n}}
&=\int_{-\infty}^{\infty}{1 \over 2\sigma}\,
\exp\pars{-\,{\verts{x - \mu} \over \sigma}}x^{n}\,\dd x
\\[3mm]&=
{1 \over 2\sigma}\bracks{%
\int_{-\infty}^{\mu}\exp\pars{x - \mu \over \sigma}x^{n}\,\dd x
+
\int_{\mu}^{\infty}\exp\pars{\mu - x\over \sigma}x^{n}\,\dd x}
\\[3mm]&=
{1 \over 2\sigma}\bracks{%
\expo{-\mu/\sigma}\sigma^{n + 1}
\int_{-\infty}^{\mu/\sigma}\expo{x}x^{n}\,\dd x
+
\expo{\mu/\sigma}\sigma^{n + 1}
\int_{\mu/\sigma}^{\infty}\expo{-x}x^{n}\,\dd x}
\\[3mm]&=
\half\,\sigma^{n}\bracks{%
\expo{-\mu/\sigma}\pars{-1}^{n + 1}
\int_{\infty}^{-\mu/\sigma}\expo{-x}x^{n}\,\dd x
+
\expo{\mu/\sigma}
\int_{\mu/\sigma}^{\infty}\expo{-x}x^{n}\,\dd x}
\\[3mm]&=
\half\,\sigma^{n}
\expo{-\mu/\sigma}\pars{-1}^{n + 1}
\bracks{-\Gamma\pars{n + 1} + \gamma\pars{n + 1,-\,{\mu \over \sigma}}}
\\[3mm]&\phantom{=}+
\\[3mm]&\phantom{=}
\half\,\sigma^{n}\expo{\mu/\sigma}
\bracks{-\gamma\pars{n + 1,{\mu \over \sigma}} + \Gamma\pars{n + 1}}
\\[3mm]&=
\half\sigma^{n}\bracks{\pars{-1}^{n}\expo{-\mu/\sigma} + \expo{\mu/\sigma}}
\Gamma\pars{n + 1}
\\[3mm]&\phantom{=}+
\\[3mm]&\phantom{=}
\half\sigma^{n}\bracks{%
\expo{-\mu/\sigma}\pars{-1}^{n + 1}\gamma\pars{n + 1,-\,{\mu \over \sigma}}
-
\expo{\mu/\sigma}\gamma\pars{n + 1,{\mu \over \sigma}}}
\end{align}
where $\Gamma\pars{z}$ is the Gamma function and $\gamma\pars{\alpha,z}$ is an incomplete gamma function.
$\Gamma\pars{2009 + 1} = 2009!$. The $\gamma$'s are approximated by
$
\gamma\pars{\alpha,x} \approx {x^{\alpha} \over \alpha}
$ when $\alpha \gg 1$. Then
$$
\gamma\pars{2009 + 1,\pm\,{\mu \over \sigma}} \approx {\pars{\pm\,\mu/\sigma}^{2010} \over 2010}
$$