Answer
$$1$$
Work Step by Step
We must integrate the integral as follows:
$$ \iint_{R} f(x,y) dA = \int_{1}^{\infty} \int_{e^{-x}}^{1} \dfrac{dy dx }{x^3y} \\= \int_{1}^{\infty}[\dfrac{\ln (1)}{x^3}-\dfrac{\ln (e^{-x})}{x^3}] dx \\=\int_{1}^{\infty} [0-\dfrac{-x}{x^3}] dx \\=[-x^{-1}]_1^{\infty} \\=0+1 \\=1$$
