Does anybody know how to calculate the integral $\displaystyle \int{\frac{lnx}{1+x}} $? Thanks.
According to Mathematica,
$\displaystyle \int{\frac{\ln{x}}{1 + x}\,dx} = \ln{x}\ln{(1 + x)} + \textrm{Li}_2(-x)$
where $\displaystyle \textrm{Li}_2(-x) = \sum_{k = 1}^{\infty}{\frac{(-x)^k}{k^2}}$
This is the Polylogarithm function, see Polylogarithm - Wikipedia, the free encyclopedia.
I do not know how it is calculated to be this function though...