1-x-ln-x-dx-0-

Question Number 43803 by vc526 last updated on 15/Sep/18

\infty

\int \frac{1}{x l n x} d x =

0

Answered by tanmay.chaudhury50@gmail.com last updated on 15/Sep/18

t = l n x

d t = \frac{d x}{x}

\int_{- \infty}^{\infty} \frac{d t}{t}

\lim_{a \to - \infty} \int_{a}^{\infty} \frac{d t}{t}

= \lim_{a \to - \infty} ∣ l n t ∣_{a}^{\infty}

= \lim_{a \to - \infty} {l n \infty - l n a}

= \lim_{a \to - \infty} {\infty - l n a}