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

## Answer this Question

## Related Questions

- calculus - Assuming that: Definite Integral of e^(-x^2) dx over [0,infinity] = ...
- Calculus AB - Evaluate the indefinite integral of (ln(x))/(x + xln(x)) dx by ...
- Calc 121 - How do you integrate using substitution: the integral from 1 to 3 of...
- Math/Calculus - How would I solve the following integral with the substitution ...
- Calculus!! - Using the identity: L{f(t)/t}=integral F(p)dp (s -->infinity), ...
- Calculus II - Evaluate using u-substitution: Integral of: 4x(tan(x^2))dx ...
- calculus please help - the actual problem is integral(2 to +infinity) (1/x^2) dx...
- calculus - how do you determine the convergence of : definite integral from 1--&...
- calculus - Find the values of p for which the following series is convergent. ...
- calc - how do you start this problem: integral of xe^(-2x) There are two ways: 1...