Integrate x^x

Math Online Tom Circle

The integration is meaningless if

$latex displaystyle {int x^{x} dx}&fg=00aa00&s=3$

unless specifying the domain of defintion, eg. interval [0,1] :

$latex displaystyle {int_{0}^{1} x^{x} dx = frac {pi^{2}}{12} }&fg=aa0000&s=3$

Note: Gamma function proof by Feynman trick : differentiate under integral.


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Author: tomcircle

Math amateur

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