# integrating of exponential of exponential function

I need the analytic answer of this integral, if possible.

I can calculate it numerically but I was wondering if an analythical solution exist.

$$\large \int_0^{+\infty}\ \frac{\text{d}x}{\large e^{a\cdot e^{b\ x}}-1}$$

Where $a, b > 0$

• i don't see a closed form solution here :/ – tired Sep 22 '16 at 20:12
• I agree with @tired. It's dubious, from my superficial look, that there is a "closed-form" answer. – Mark Viola Sep 22 '16 at 20:16
• point is that the a series expansion yields an infinite sum of incomplete beta functions which are highly unlikely to add up to something which contains known functions only – tired Sep 22 '16 at 20:17