Question Number 159532 by HongKing last updated on 18/Nov/21
$$\mathrm{if}\:\:\mathrm{0}<\mathrm{a}\leqslant\mathrm{b}\:\:\mathrm{then}: \\ $$$$\underset{\:\boldsymbol{\mathrm{a}}} {\overset{\:\boldsymbol{\mathrm{b}}} {\int}}\:\frac{\mathrm{x}^{\mathrm{19}} }{\:\sqrt{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{30}} }}\:\mathrm{dx}\:\geqslant\:\mathrm{log}\:\sqrt[{\mathrm{10}}]{\frac{\mathrm{2}\:+\:\mathrm{b}^{\mathrm{20}} }{\mathrm{2}\:+\:\mathrm{a}^{\mathrm{20}} }} \\ $$$$ \\ $$