In my old writes I found next formula, where is ${_{}^2}x$ is tetration:
$\int_0^1 {_{}^2}x \ dx = \sum\limits_{i=1}^\infty \frac {(-1)^{i+1}} {{_{}^2}i} \approx 0.783430511\ldots$
And now I am interested in series of generalized case of tetration:
$\int_0^1 {_{}^n}x \ dx = ?$
Could anybody find out it with explanation?