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.

**DEMO**: