Question: Analytic integral of ln(x)*ln(1-x)^2

Hi all,

I would like to know how can I teach Maple to do the analytic integral of ln(x)*ln(1-x)^2 for x in [0,1] ]which has a solution of -6+Pi^2/3+2*Zeta(3) ~ -0.306018 (from Mathematica). I want this because I have to integrate an expression which has terms of this type and with similar x dependence with this being the simplest example.

I don't  think Maple has a closed form for this integral because when I use the command integrate(ln(x)*ln(1-x)^2,x=0..1) the output returns the function called.


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