The question is as follows:
Show that $\frac{1}{x^x}$ is continuous on $[0,1]$, and that its integral on this range is equal to $\sum\frac{1}{n^n}$ from $n=1$ to $n=\infty$.
The question also provides the following hint:
Write $\frac{1}{x^x} = \sum\frac{(-xlogx)^n}{n!}$ from $n=0$ to $n= \infty$.
Thanks so much for any help! :)