# How to prove $\int_0^1\frac{\mathrm{d}x}{x^x}=\sum_{k=1}^\infty \frac1{k^k}$? [duplicate]

I've found this wonderful identity here.

On the first spot it seems for me true, but I don't have any idea, how could it be proven. In simpler form: "how the hell...?" :-)