Question Number 215081 by MrGaster last updated on 28/Dec/24
$$ \\ $$$$\mathrm{prove}: \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{\left(\mathrm{ln}\left({x}/\left(\mathrm{1}+{x}\right)\right)^{\mathrm{4}} \mathrm{ln}\left({x}^{\mathrm{3}} \left(\mathrm{1}+{x}\right)^{\mathrm{17}} \right.\right.}{\mathrm{1}+{x}}{dx}=−\mathrm{240}\zeta\left(\mathrm{3}\right)^{\mathrm{2}} \\ $$$$ \\ $$