(11/25/2013, 09:59 PM)Ryan Wrote: Hi,Hi Ryan/Hi razrushil -

I was wondering that I might have found a solution for the integral x^x.

The solution is very complicated and has an infinite number of terms but I would like to know if it can be useful in mathematics.

Assuming I found the correct solution, does this mean anything?

Ryan

Hmm, I don't see how this can be *specially* useful for tetration (everything can of course be somehow useful). The integration here would be related to the variability in the two occurences of x; but the interesting feature of tetration seems to me, that it has variability/an indeterminate in the number, the "height", of the iteration - and it would be especially interesting if there was an integration with respect to that height-parameter assuming a constant exponential base.

As far as I recall, that integral is also shown at "mathworld" see http://mathworld.wolfram.com/SophomoresDream.html

Gottfried

Gottfried Helms, Kassel