Hinweis.

(1)
Zeige, daß $ \mbox{$\int_0^1 x^m (\log x)^n\,{\mbox{d}}x = (-1)^n {\displaystyle\frac{n!}{(m+1)^{n+1}}}$}$.
(2)
Schreibe $ \mbox{$x^x = \sum_{k = 0}^\infty {\displaystyle\frac{x^k(\log x)^k}{k!}}$}$.