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 Integration of x^x Ryan Newbie Posts: 1 Threads: 1 Joined: Nov 2013   11/25/2013, 09:59 PM 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 razrushil Junior Fellow Posts: 3 Threads: 0 Joined: Feb 2014 02/24/2014, 06:10 AM 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. Gottfried Ultimate Fellow Posts: 768 Threads: 120 Joined: Aug 2007 02/25/2014, 08:28 AM (This post was last modified: 02/25/2014, 08:32 AM by Gottfried.) (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? RyanHi 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 Gottfried Helms, Kassel « Next Oldest | Next Newest »

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