9.2.12 Integrals depending on a parameter

Problem: Applying differentiation with respect to the parameter, calculate the following integral: \[ \begin{array}{l} I=\int_{0}^{+\infty} \frac{e^{-\alpha x}-e^{-\beta x}}{x} \sin m x d x, \\ \alpha>0, \quad \beta>0, \quad m \neq 0 . \end{array} \]