How would you solve the following?
$$\int^1_0 \frac{\operatorname{Li}_2(-x)}{x} \log(1+x)\, \mathrm dx$$
2026-03-26 01:03:36.1774487016
Evaluating $\int^1_0 \frac{\operatorname{Li}_2(-x)}{x} \log(1+x)\, \mathrm dx$
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Hint
$$\int \frac{\log(1+x)}{x} \, \mathrm dx=-\text{Li}_2(-x)$$
Added later
Using the trick given in the hint, then $$\int \frac{\operatorname{Li}_2(-x)}{x} \log(1+x)\, \mathrm dx=-\frac{\text{Li}_2(-x){}^2}{2}$$ and so $$\int^1_0 \frac{\operatorname{Li}_2(-x)}{x} \log(1+x)\, \mathrm dx=-\frac{\pi ^4}{288}$$