evaluating $\int_0^{\infty}\frac{e^{-t-\frac{x}{t}}}{t} dt$ I got to this integral, while proving some theorem in statistics:
$$\int_0^\infty \frac{e^{-t-\frac{x}{t}}}{t} \mathop{dt}$$
I have trouble evaluating it. I tried partial integration, tried substitution with some polynomial and some trigonometric functions. None of them helped, and Wolfram can't compute it either. Do you have a hint on how to solve this?

With a little help from Maple, the integral is
$$\int_0^\infty \frac{e^{-t-\frac{x}{t}}}{t}\,dt = 2K_0(2\sqrt{x}),$$
where $K_0$ is the modified Bessel function of the second kind of order zero.
