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Category: Matrices and Determinants

Prove-that-lim-n-ln-2-n-2-n-0-lnt-1-t-2-dt-pi-2-6-ln-2-2-

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Question Number 222418 by Jgrads last updated on 26/Jun/25 $$\mathrm{Prove}\:\mathrm{that}:\: \\ $$$$\underset{\mathrm{n}\rightarrow+\infty} {\mathrm{lim}}\:\left[\:\mathrm{ln}^{\mathrm{2}} \left(\mathrm{n}\right)−\mathrm{2}\underset{\:\mathrm{0}} {\int}^{\:\mathrm{n}} \frac{\mathrm{lnt}}{\:\sqrt{\mathrm{1}+\mathrm{t}^{\mathrm{2}} }}\:\mathrm{dt}\:\right]=\:\frac{\pi^{\mathrm{2}} }{\mathrm{6}}+\mathrm{ln}^{\mathrm{2}} \left(\mathrm{2}\right) \\ $$ Answered by MrGaster last…

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