how to double integrate this exponential function how can i integrate this $\int_0^∞\int_x^∞{\frac{e^{-y}}{y}}dy dx$
i am stuck here $\int{\frac{e^{-y}}{y}}dy$. I have tried some log substitutions.

There is no elementary antiderivative of $e^{-y}/y$

A much better approach, since the integrands are positive, is to change the order of integration: This leads to
$$\int_0^{\infty} \int_0^y \frac{e^{-y}}{y} dx dy = \int_0^{\infty} \frac{e^{-y}}{y} y dy$$
