How can I prove that $$\int_{0}^{1} \ln x \ln(1-x)dx = 2-\frac{\pi^2}{6}$$
I could not find an antiderivative for $f(x)=\ln x \ln(1-x)$. I was thinking to add a parameter but did not see a useful place where to add it. Any further suggestions?
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1It's a duplicate of Evaluate $ \int_{0}^{1} \ln(x)\ln(1-x),dx $. See also: https://math.stackexchange.com/q/1414022/515527 – Zacky Nov 29 '19 at 22:20
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1@Nyssa - oh thank you, I was looking for this – ThomasL Nov 29 '19 at 22:27