calculus - Best way to integrate $ int_0^infty frac{e^{-at} - e^{-bt}}{t} text{d}t $

Today I had an exam and I mixed up the integration by parts formula.
The question was to integrate
$$ \int\nolimits_0^\infty \frac{e^{-at} - e^{-bt}}{t} \text{d}t $$

I will try solve this again with the right formula when I arrive home. I would appreciate if somebody could tell me the solution so I can double check and maybe give a hint to another way of solving this instead of integration by parts (if possible).