Prove-that-0-ln-t-1-t-2-t-dt-pi-2-2-

Question Number 197113 by Erico last updated on 08/Sep/23

Prove that

{\int_{0}}^{+ \infty} (\frac{l n (t + \sqrt{1 + t^{2}})}{t}) d t = \frac{π^{2}}{2}

Answered by witcher3 last updated on 08/Sep/23

\ln (t + \sqrt{1 + t^{2}}) > 2, \forall x ⩾ e

\int_{2}^{\infty} \frac{\ln (t + \sqrt{t^{2} + 1})}{t} ⩾ \int_{2}^{\infty} \frac{2}{t} dt = \infty integral didnt cv

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