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Question Number 108282 by Ar Brandon last updated on 16/Aug/20

Determine the nature of the integral  ∫_2 ^(+∞) (√(t^2 +3t)) ln(cos((1/t))) sin^2 ((1/(ln(t))))dt

$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{nature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{integral} \\ $$$$\int_{\mathrm{2}} ^{+\infty} \sqrt{\mathrm{t}^{\mathrm{2}} +\mathrm{3t}}\:\mathrm{ln}\left(\mathrm{cos}\left(\frac{\mathrm{1}}{\mathrm{t}}\right)\right)\:\mathrm{sin}^{\mathrm{2}} \left(\frac{\mathrm{1}}{\mathrm{ln}\left(\mathrm{t}\right)}\right)\mathrm{dt} \\ $$

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