$\displaystyle \int{\frac{1}{\log \left( \log \left( \log x \right) \right)}dx}=$...
Hi inoid !
The function 1/ln(ln(ln(x))) is integrable as x>e because continuous.
But the integral cannot be expressed in terms of a finite number of usual functions. What is more, I doubt that it could be expressed with a finite number of standard special functions.