Question Number 223534 by Tawa11 last updated on 28/Jul/25
$$\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{ln}^{\mathrm{3}} \left(\frac{\mathrm{1}\:\:−\:\:\mathrm{x}}{\mathrm{1}\:\:+\:\:\mathrm{x}}\right)\:\mathrm{dx} \\ $$
Answered by MathematicalUser2357 last updated on 31/Jul/25
$$ \underset{{x}\rightarrow\mathrm{1}^{−} } {\mathrm{lim}}\int−\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{lim}}\int\: \mathrm{1}.\mathrm{67344} \\ $$
Commented by Tawa11 last updated on 02/Aug/25
$$\mathrm{Answer}\:\mathrm{is}\:\:=\:\:\frac{\mathrm{93}}{\mathrm{8}}\zeta\left(\mathrm{5}\right)\:\:−\:\:\frac{\mathrm{7}\pi^{\mathrm{2}} }{\mathrm{8}}\zeta\left(\mathrm{3}\right) \\ $$