Question

(integral from 1 to infinity) [ln(x)]/(x)

Answer 1

try the sub u=ln(x)

Answer 2

I want to know if it converges or diverges

Answer 3

Well we need to integrate first

Answer 4

yeah the antiderivative i got was (1/2)(ln(x))^2 and then I solved it as the limit as b approaches infinity evaluating it from 1 to b. The answer i got was that it diverges but I'm not sure if that is right.

Answer 5

\[\lim_{b \rightarrow \infty}(\frac{\ln(b))^2}{2}-\frac{\ln(1))^2}{2})=\lim_{b \rightarrow \infty}\frac{(\ln(b))^2}{2}\]

Answer 6

well ln(b)->inf as b->inf

Answer 7

squaring that gets you bigger numbers quicker

Answer 8

I agree with the diverges

Answer 9

yeeeeesssssssssss!!! thank you so much!