I need to calculate the integral of
$$\int_{0}^{u}e^{-\alpha t-\frac{\beta}{t}}dt$$
From one book I came to knnow
$$\int_{0}^{\infty} e^{-\alpha t-\frac{\beta}{4t}}dt = \sqrt{\frac{\beta}{\alpha}}K_1(\sqrt{\beta\alpha}) $$
where $K_1(.)$ is first order modified Bessel function of second kind.