# Solve the following integral: int_0^(oo) 1/x e^(-x/a) (e^(-e^(-((x−c)/(b)))))dx

Solve the following integral:
${\int }_{0}^{\mathrm{\infty }}\frac{1}{x}{\mathrm{e}}^{-\frac{x}{a}}\left({\mathrm{e}}^{-{\mathrm{e}}^{-\left(\frac{x-c}{b}\right)}}\right)dx$
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.
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allelog5
The integral won't converge, because
${\mathrm{e}}^{-\frac{x}{a}}\left({\mathrm{e}}^{-{\mathrm{e}}^{-\left(\frac{x-c}{b}\right)}}\right)={\mathrm{e}}^{-{\mathrm{e}}^{\frac{c}{b}}}+o\left(1\right)$
Around 0.