I'm currently trying to calculate a weird gaussian integral:
$$ \int\limits\_{\mathbb{R}^3} \mathrm{d}^3\vec x \ |\vec x| \exp( -a \cdot x^2) $$
where $a > 0$ of course.

I can easily evaluate it if there is only $x\_1, x\_2$ or $x\_3$ or products of those in front of the exponential function. But I have now idea how to seperate $|\vec x| = \sqrt{ x\_1 + x\_2 + x\_3}$.

any ideas?