Expectation of Logistic Distribution/Lemma 3

Lemma for Expectation of Logistic Distribution

 * $\forall k \in \N$:


 * $\ds \int_{\to 0}^{\to 1} \map {\ln^{2k + 1} } {\dfrac {1 - u} u} \rd u = 0$

Proof
let:

Then: