lim-x-1-lnx-0-x-dt-lnt-

Question Number 91228 by ~blr237~ last updated on 28/Apr/20

\lim_{x \to 1} l n x (\int_{0}^{x} \frac{d t}{l n t})

Commented by abdomathmax last updated on 29/Apr/20

= {l i m}_{x \to 1} (x - 1) l n x \times \frac{\int_{0}^{x} \frac{1}{l n t} d t}{x - 1}

w e h a v e {l i m}_{x \to 1} (x - 1) l n x = 0

{l i m}_{x \to 1} \frac{\int_{0}^{x} \frac{1}{l n t} d t}{x - 1} = {l i m}_{x \to 1} \frac{\frac{1}{l n x}}{1} (h o s p i t a l)

= {l i m}_{x \to 1} \frac{1}{l n x} = \infty . p e r h a p s t h i s l i m i t d o n t e x i s t . .