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.

Thank you for your help.


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 $0$.

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  • $\begingroup$ Thank you, great help! @Botond $\endgroup$ – Mina Kay Nak Jan 6 at 14:10

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