integration - Evaluation of integral using laplace transform

How to evaluate the integral $\displaystyle\int_0^\infty\frac{e^{-at}-e^{-bt}}{t}dt$?
As this is Laplace transform of $\frac{1}{t}$ at $s=a$,

I tried with division by $t$ property, i.e. division by $t$ and integration from $s$ to infinity, but I am getting stuck at diverging integral of $\log s$ from $0$ to $\infty$. (Laplace transform of $\frac{1}{t}$ is $\int_0^\infty \frac{1}{s}ds=\log s$.

Please help