# Variance of Logistic Distribution/Lemma 2

$\ds \int_{\to 0}^{\to 1} \map {\ln^2} u \rd u = 2$
 $\ds \int_{\to 0}^{\to 1} \map {\ln^2} u \rd u$ $=$ $\ds \bigintlimits {u \ln^2 u } 0 1 - 2 \int_{\to 0}^{\to 1} \map \ln u \rd u$ Primitive of Power of Logarithm of x $\ds$ $=$ $\ds \paren {\paren {0 - 0} - 2 \paren {-1} }$ Expectation of Logistic Distribution:Lemma 2 $\ds$ $=$ $\ds 2$
$\blacksquare$