Solution
= Solution
The <divergence> is $y^2+x^2+z^2=r^2$. In <spherical coordinates>, the angular integral is $4\pi$ and the <volume element> contributes $r^2\,dr$. Thus
$$
\boxed{\iiint_{r\leq R}\nabla\cdot\mathbf F\,dV
=4\pi\int_0^R r^4\,dr=\frac{4\pi R^5}{5}}.
$$