How to Approach a Double Exponential Integral?

[Steve Zissou]

TL;DR Summary

How to approach this? Integrating a double exponential

Hello frens,

How should one approach this sort of integral? Any tips would be appreciated.

Let's say we have

$$ \int_{(1)}^{(2)}\exp\left[ a+b\exp\left[ f(x) \right] \right]dx$$

...where the limits of integration are not important.

Any tips? Thanks!

 

[Frabjous]

Try substituting ln(z)=f(x)

 

[fresh_42]

I get $\displaystyle{e^a\int \dfrac{c^u}{u \cdot\dfrac{d}{dx}f(x)}}\,du$ so I need more information about $f',$ with $c=e^b\ ,\ u=\exp(f(x)).$

 

[Steve Zissou]

fresh_42 Thank you, I will make my problem a little more..."firm."