Question

how to start improper integral from 1 to infinity of
(ln(x))/x dx?

Answer 1

To start? Hmm I guess to start we should write it in a more acceptable form:\[\Large \int\limits_1^{\infty}\frac{\ln x}{x}\;dx\quad=\quad \lim_{b\to \infty}\int\limits_1^b\frac{\ln x}{x}\;dx\]

Answer 2

Actually let's write it like this:\[\Large \lim_{b\to \infty}\int\limits\limits\limits_1^b \ln x\left(\frac{1}{x}\;dx\right)\]

Answer 3

We're going to do a u-sub, this might make it easier to identify the parts :)

Answer 4

should i use integration by parts to continue?

Answer 5

o..ok

Answer 6

u = lnx
what do you get for du? :)

Answer 7

1/x ?

Answer 8

\[\Large du\quad=\quad\frac{1}{x}dx\]Hmm don't forget the differential! :O

Answer 9

Understand how to use those two pieces to make the substitution?\[\Large \lim_{b\to \infty}\int\limits\limits\limits\limits_1^b \ln x\left(\frac{1}{x}\;dx\right)\]