Solution
= Solution
For a spherically symmetric <mass density>, the angular integral in <spherical coordinates> is $4\pi$. The two disjoint shell contributions therefore give the <mass>
$$
M=4\pi\int_a^b r^2\,dr+4\pi\int_c^d r^{-2}\,dr,
$$
so
$$
\boxed{M=4\pi\left[\frac{b^3-a^3}{3}+\frac1c-\frac1d\right]}.
$$
Both contributions are positive because $a<b$ and $c<d$.