Integral of 1/(x*ln(x)) converging or diverging?

1. May 4, 2006

ndnbolla

In order to find the integral of 1/(x*ln(x)) dx, I tried using the substitution method where

u = 1/x and dv = 1/ln(x) dx .

Then du = ln(x) dx.

However this is where I got stuck.

What would v equal? Or is their another way I should be approaching this integral in order to find if it is diverging or converging and if converging, to what value?

2. May 4, 2006

siddharth

First of all, is it a definite integral? What are the limits of integration?

Then, if u=1/x then du is not ln(x) dx. Why don't you try the substitution u=ln(x) and see what happens?

3. May 4, 2006

ndnbolla

My mistake and sorry for not mentioning the limits. Its an improper integral with lower limit 2 and upper limit infinity.

I think I found the solution...

u=ln(x)
du=(1/x)

int(1/u) du

And then solve for the integral, with the lower limit being ln(2) and the upper limit being infinity.

It ends up diverging, correct?

4. May 5, 2006

siddharth

Yes, I think you're right.