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\section{Introduction}  When confronted with an integral of the form \begin{equation}  \int_{-\intfy}^{\infty} e^{-ax^2} \;dx = \sqrt{\frac{\pi}{a}}  \end{equation}  There is a standard trick to take the derivative with respect to the parameter $a$ such that \begin{equation}  \frac{d}{da}\int_{-\intfy}^{\infty} e^{-ax^2} \;dx = \frac{d}{da}\sqrt{\frac{\pi}{a}} \\  \int_{-\intfy}^{\infty} x^2e^{-ax^2} \;dx = \frac{1}{2}\sqrt{\frac{\pi}{a^3}}  \end{equation}