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).