calculus

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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 -

    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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