Chapter 5.4, Problem 215E

In the following exercises, use two circular permutations of the variables x. y. and z to write new integrals whose values equal the value of the original integral. A circular permutation of x. y. and z is the arrangement of the numbers in one of the following orders: y, z, and x or z, x. and y.

215. ${\displaystyle \underset{0}{\overset{1}{\int }}{\displaystyle \underset{1}{\overset{3}{\int }}{\displaystyle \underset{2}{\overset{4}{\int }}\left(x^2{z}^2+1\right)dxdydz}}}$