- E26
[1C2]Prerequisites:[1C0].Difficulty:**.Show identities
\begin{align} β«_ 0^ 1 x^{-x}\, dx & = β_{n=1}^β n^{-n}& & (=\sim 1.291285997\dots ) \\ {} β«_ 0^ 1 x^ x \, dx & = β_{n=1}^β (-1)^{n+1}n^{-n} & & (=\sim 0.783430510712\dots ) \end{align}(Hint: use the Taylor series \(e^ z\), and substitute \(z=x\log (x)\); use the exercise [1C0] above.)
EDB β 1C2
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Authors:
"Mennucci , Andrea C. G."
.
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