# integral of exponentials

I have difficulties to solve the following integral:

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

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.

The integral won't converge, because $$\mathrm{e}^{-\frac{x}{a}} (\mathrm{e}^{-\mathrm{e}^{-(\frac{x-c}{b})}}) = \mathrm{e}^{-\mathrm{e}^{\frac{c}{b}}}+o(1)$$ Around $$0$$.