I need to find , $$\int_{0}^{\infty} \int_{0}^{\infty} \frac{e^{-(x+y)}}{x+y} dxdy$$
My attempt:
I tried doing integration wrt x first then substitute $t = x+y$, $$ \int_{0}^{\infty} e^{-y} \left( \int_{0}^{\infty} \frac{e^{-x}}{x+y} dx\right) dy = \int_{0}^{\infty} e^{-y} \left( \int_{t=y}^{\infty} \frac{e^{-(t-y)}}{t} dt\right) = \int_{0}^{\infty} \int_{t=y}^{\infty} \frac{e^{-t}}{t} dt $$
I don't know how to proceed further. Any hint on how should i tackle this kind of problem would be appreciated ...