Chapter 15.8, Problem 43E

Evaluate the integral by changing to spherical coordinates.

43. ${\displaystyle {\int }_{-2}^2}{\displaystyle {\int }_{-\sqrt{4-x^2}}^{\sqrt{4-x^2}}}{\displaystyle {\int }_{2-\sqrt{4-x^2-y^2}}^{2+\sqrt{4-x^2-y^2}}}$ (xz + yz + z²)^3/2 dz dy dx