I have problem in order to compute the integral $$\int_0^\infty dx \left(\frac{e^{-iax} - e^{-ibx}}{x}\right) $$
The result should be \begin{align} \int_0^\infty dx \left(\frac{e^{-iax} - e^{-ibx}}{x}\right) = \begin{cases} -\ln\left(\displaystyle{\frac{a}{b}}\right), \quad \quad \quad a>b \\ -\ln\left(\displaystyle{\frac{a}{b}}\right) + i\pi, \quad a<b \end{cases} \end{align}
I don't know which contour taken in order to achieve this result.
