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:<math>\begin{align}
\int_{-\infty}^\infty \exp\left( -{1 \over 2} a x^2 + Jx\right) \, dx &= \exp\left( { J^2 \over 2a } \right ) \int_{-\infty}^\infty \exp \left [ -{1 \over 2} a \left ( x - { J \over a } \right )^2 \right ] \, dx \\[8pt]
&= \exp\left( { J^2 \over 2a } \right )\int_{-\infty}^\infty \exp\left( -{1 \over 2}
&= \left ( {2\pi \over a } \right ) ^{1\over 2} \exp\left( { J^2 \over 2a }\right )
\end{align}</math>
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