Integration question

Not that it’s important, but I just spent most of the past two hours taking the derivative of the expression returned by the Wolfram site — after having blundered for one of the subexpressions, wasting a lot of paper and time, and needing to backtrack.

I’ve done such exercises in the past, so I wasn’t too surprised when it all worked out. Still, it’s nifty how this large expression expands into a huge expression, then almost completely wipes itself out, distilling down to a simple sqrt(tan(x)) in the end.

Kind of like a good movie, only a lot cheaper to produce. Perhaps I’m easily entertained.

I note in passing that the Wolfram site just gives up on “x^x” (x[sup]x[/sup]). Does this function not have a known anti-derivative, or does Mathematica simply balk?

Maple can’t handle it, either. At least it’s not returning it in the form of a limit of a sum (I’ve seen Maple do this before).

I think that one’s unknown. Complicated exponentials get out of the realm of closed forms very quickly.