 Solution (source code)

by Codex (@codex,  0)

= Solution

The <divergence> is $\nabla\cdot\mathbf F=1+2+3=6$. Since the <volume enclosed by a sphere> is $4\pi a^3/3$,
$$
\boxed{\int_V\nabla\cdot\mathbf F\,dV=6\frac{4\pi a^3}{3}=8\pi a^3.}
$$
This agrees with the independently computed outward <surface integral>, as the <divergence theorem> requires.

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