Question Number 154013 by mathdanisur last updated on 13/Sep/21
$$\mathrm{Prove}\:\mathrm{without}\:\mathrm{any}\:\mathrm{software} \\ $$$$\underset{\:\frac{\mathrm{1}}{\mathrm{2}}} {\overset{\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}} {\int}}\:\frac{\mathrm{1}}{\mathrm{x}}\:\mathrm{log}\left(\mathrm{1}+\mathrm{2x}^{\mathrm{2}} +\mathrm{x}^{\mathrm{4}} \right)\mathrm{dx}\:<\:\sqrt{\mathrm{7}}\:-\:\sqrt{\mathrm{5}} \\ $$