# Expectation of Logistic Distribution/Lemma 1

$\ds \int_{\to 0}^{\to 1} \map \ln {1 - u} \rd u = -1$
 $\ds \int_{\to 0}^{\to 1} \map \ln {1 - u} \rd u$ $=$ $\ds \bigintlimits {\paren {u - 1} \map \ln {1 - u} - u } 0 1$ Corollary to Primitive of Logarithm of x $\ds$ $=$ $\ds \paren {\paren {0 - 1} - \paren {0 - 0} }$ $\ds$ $=$ $\ds -1$
$\blacksquare$