# Tetration Forum

Full Version: Integration of x^x
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Hi,

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
I can't say whether it is useful, but it most likely won't be if you can't write it in shorter notation. I've seen something like this elsewhere, but terms were just written out and there didn't seem to be much of a pattern, at least at first glance.
If your results can be generalized more it can be like an integral for general tetration. This would be more difficult, but it has to start somewhere.
(11/25/2013, 09:59 PM)Ryan Wrote: [ -> ]Hi,

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
Hi Ryan/Hi razrushil -

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