Volume integral, spherical conditions, finding density

Nov 2019
Can anyone help please?

A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on the origin.
The shell is made of a material with density
ρ =( A*x^2 * z ^2) /(x^2 + y^2 + z^2) ^2 , where A is a constant.
find the mass M of the shell by evaluating a suitable volume integral.

I know that the density is

and that the volume integral should be given by the integral of A*sin^2(theta)*cos^2(phi)*cos^2(theta)*r^2*sin(theta)

but not sure where to go from here?

Thanks in advance.