Posted by **sarah** on Wednesday, February 6, 2008 at 8:21pm.

what is the answer for the integral of

(1/(xln(x)) from 1 to infinity?

I first found the integral using u substitution- so u=ln(x) and du=1/x*dx

this gave my du/u,leading to the ln(u)

=ln(ln(x)) from 1 to infinity

then I did the limit as t approaches infinity of 1/(tln(t)) - ln(ln(1))

my answer was that the function diverges, because the above limit is going to infinity. Is this right?

- calculus -
**Damon**, Wednesday, February 6, 2008 at 8:36pm
dx/(x ln x)

let u = ln x

then du = dx/x

so indeed

du/u

which is ln u

now when x = 1, u = 0

and when x = infinity , u = infinity

Yes, I get does not converge

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