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Question Number 199511 by SANOGO last updated on 04/Nov/23

$${\int }_1^{+oo}ln{(1+lnx)}^{-lnx}dx$$

Commented by SANOGO last updated on 04/Nov/23

$$thankyou$$

Answered by witcher3 last updated on 04/Nov/23

$$\mathrm{diverge}$$$$\ln {(1+\ln \left(\mathrm{x}\right))}^{-\ln \left(\mathrm{x}\right)}=\ln \left(\frac{1}{(1+\ln {\left(\mathrm{x}\right)}^{\ln \left(\mathrm{x}\right)}}\right)$$$$\mathrm{\forall }\mathrm{x}⩾\mathrm{e}$$$$\ln \left(\frac{1}{{(1+\ln \left(\mathrm{x}\right))}^{\ln \left(\mathrm{x}\right)}}\right)⩽\ln \left(\frac{1}{2^2}\right)⩽-\ln \left(4\right)$$$$\mathrm{diverge}-\mathrm{\infty }$$

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