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Tagged with polylogarithmic-integral closed-form
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How to evaluate $\int_0^1 \frac{\arctan(x)}{x} \ln^2(1 - x) \, dx$
Question
How to evaluate $$\int_0^1 \frac{\arctan(x)}{x} \ln^2(1 - x) \, dx$$
My attempt
\begin{align}
\int_0^1 \frac{\arctan(x)}{x} \ln^2(1 - x) \, dx &= \int_0^1 \int_0^1 \frac{\ln^2(1 - x)}{...
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33
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7
answers
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Evaluating $\int_0^1 \frac{\log x \log \left(1-x^4 \right)}{1+x^2}dx$
I am trying to prove that
\begin{equation}
\int_{0}^{1}\frac{\log\left(x\right)
\log\left(\,{1 - x^{4}}\,\right)}{1 + x^{2}}
\,\mathrm{d}x = \frac{\pi^{3}}{16} - 3\mathrm{G}\log\left(2\right)
\tag{1}
\...
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