Question Number 153808 by mathdanisur last updated on 10/Sep/21
$$\mathrm{If}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}<\mathrm{1}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\left(\frac{\mathrm{1}\:-\:\mathrm{xyz}}{\mathrm{1}\:+\:\mathrm{xyz}}\right)^{\mathrm{3}} \mathrm{dxdydz}\:\geqslant\:\left(\underset{\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\frac{\mathrm{1}\:-\:\mathrm{x}^{\mathrm{3}} }{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{3}} }\:\mathrm{dx}\right)^{\mathrm{3}} \\ $$