Answer
$1$
Work Step by Step
Consider $I=\int_{1}^{e} \int_{1}^{x} \int_{0}^{z} (\dfrac{2y}{z^3}) \ dy \ dz \ dx$
or, $=\int_{1}^{e} \int_{1}^{x} \dfrac{1}{z} \ dz \ dx$
or, $=\int_{1}^{e} [\ln (x)] \ dx$
or, $=[ x \ln x -x]_1^e$
or, $=[x(\ln x-1)]_1^e$
or, $=(e-1)[(\ln e-\ln 1)-1]$
or, $=1$
