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A cube $[0,1] \times [0,1] \times [0,1]$ has mass density $\rho(x,y,z)=(x+1)e^z y$, find the total mass of the cube.

$1$

$\cfrac{1}{2}$

$\cfrac{3}{4}$

$\cfrac{1}{8}$

$\cfrac{1}{e}$