Solve the following integral:

$${\int}_{0}^{\mathrm{\infty}}\frac{1}{x}{\mathrm{e}}^{-\frac{x}{a}}({\mathrm{e}}^{-{\mathrm{e}}^{-(\frac{x-c}{b})}})dx$$

I wanted to compute it by using Laplace Transform, but $\frac{1}{x}$ part made me confused and I could not reach to a solution.

$${\int}_{0}^{\mathrm{\infty}}\frac{1}{x}{\mathrm{e}}^{-\frac{x}{a}}({\mathrm{e}}^{-{\mathrm{e}}^{-(\frac{x-c}{b})}})dx$$

I wanted to compute it by using Laplace Transform, but $\frac{1}{x}$ part made me confused and I could not reach to a solution.