How to evaluate $ \int_0^1 {\log x \log(1-x) \log^2(1+x) \over x} \,dx $ [duplicate]
Solve that the following integral: $$ \int_0^1 {\log x \log(1-x) \log^2(1+x) \over x} \,dx. $$
I haven't solved it yet.
You can find my solution here.
My argument here is greatly simplified by the use of complex analysis, thanks to the user Random Variable. So you may also want to check it, too.