I'm bored today so I tried to integratel $\displaystyle x^x$, but I couldn't. How do you integrate that?

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- Apr 25th 2009, 03:52 PMchengbinHow to integrate x^x?
I'm bored today so I tried to integratel $\displaystyle x^x$, but I couldn't. How do you integrate that?

- Apr 25th 2009, 03:56 PMChop Suey
You can't express it in elementary functions.

- Apr 25th 2009, 03:59 PMchengbin
- Apr 25th 2009, 04:05 PMKrizalid
it means that you'll never find a certain function whose derivative yields the integrand.

- Apr 25th 2009, 05:24 PMmr fantastic
Actually it's not difficult. It's just that nobody bothered to think of defining a special function to account for its antiderivative.

There is a solution - the function F such that dF/dx is x^x. This function is also known as the Fantastic F-function.

It can't be written anymore nicely than that. There is nothing surprising about this. Almost no functions have integrals that can be written out nicely and explicitly in some closed form. - Apr 25th 2009, 07:51 PMcurvature
See this for elementary functions:

Elementary function - Wikipedia, the free encyclopedia