Spence's Integral

$\begin{figure}\begin{center}\BoxedEPSF{SpencesIntegral.epsf scaled 700}\end{center}\end{figure}$

$\begin{displaymath} F(x) = \mathop{\rm Li}\nolimits _2(1-x) =\int_{1-x}^0 {\ln(1-t)\over t}\,dt, \end{displaymath}$

where $\mathop{\rm Li}\nolimits _2(x)$ is the Dilogarithm.