[tex]\int x^xdx[/tex](adsbygoogle = window.adsbygoogle || []).push({});

After calculus today, our professor casually asked us to integrate the above problem. Most of us stated DNE (does not exist), or possibly x+1 / x+1 . He stated that both of these solutions were incorrect and than challenged us to write a paper on the subject which seemed ridiculous to me but here I am.

So a few questions...

Can this be done by Taylor Series expansion??

[tex]\int x^x dx=x + \frac{\left( -1 + 2\,\log (x) \right) \, x^2}{4} + \frac{\left( 2 - 6\,\log (x) + 9\,{\log (x)}^2 \right) \,x^3}{54} + \frac{\left( -3 + 12\,\log (x) - 24\,{\log (x)}^2 + 32\,{\log (x)}^3 \right) \,x^4}{768} + \frac{\left( 24 - 120\,\log (x) + 300\,{\log (x)}^2 - 500\,{\log (x)}^3 + 625\,{\log (x)}^4 \right) \,x^5}{75000} + \frac{\left( -5 + 30\,\log (x) - 90\,{\log (x)}^2 + 180\,{\log (x)}^3 - 270\,{\log (x)}^4 + 324\,{\log (x)}^5 \right) \,x^6}{233280} + {O(x^7)[/tex]

or is the answer simply dF/dx is x^x ???

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# Integrating x^x

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