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Prove-without-any-software-1-2-3-2-1-x-log-1-2x-2-x-4-dx-lt-7-5-




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

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