I have accrossed in my text book this integral :$ \int_{0}^{1}\frac{\log^2 (x+1)}{x}$ and i used integration by part but i can't get any result compatible with wolfram alpha , i'm really confused how this integral had a relationship with polylogarithm function and why it's closed form result depend to the Riemann zeta function , function which i didn't know before, then my question is : how do i evaluate this integral : $$ \int_{0}^{1}\frac{\log^2 (x+1)}{x}$$ ?
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I think you have idea about polylogarithms $Li$ i.e. Jonquiere function. – Akash Roy Apr 23 '18 at 18:16
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Here you can find expression for more general case. – user Apr 23 '18 at 18:46