f_Z(z)=\int_{\mathbb{R}}f_{\frac{x}{Y}}(z|x)f_X(x)dx=\int_{[0,1]}e^{-\frac{x}{z}}\frac{x}{z}d\frac{x}{z}=\{\frac{x}{z}=y\}=\int_{[0,z^{-1}]}e^{-y}ydy