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Thread: Improper Integral of 1/(xln(x)) from e to infinity help?

  1. #1

    Improper Integral of 1/(xln(x)) from e to infinity help?

    So the problem is [tex]\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}[/tex]

    I know I would need to get the limit from n to infinity and swap infinity in the integral with n.
    I don't know what to do with (1/(xlnx))dx . I cant do by sums and wen I do by parts I cant find dv which I set to ln(x)^(-1)dx. Im just not sure where to go with this...
    Last edited by stapel; 10-26-2014 at 08:49 AM. Reason: Typing out text in graphic.

  2. #2
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    Quote Originally Posted by imattxc View Post
    So the problem is [tex]\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}[/tex]
    What is the derivative of [tex]\log((\log(x)))~?[/tex]
    Last edited by stapel; 10-26-2014 at 08:49 AM. Reason: Copying typed-out text into reply.
    “A professor is someone who talks in someone else’s sleep”
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  3. #3
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    Quote Originally Posted by imattxc View Post
    So the problem is [tex]\displaystyle{\int_e^{\infty}\, \frac{1}{x\, \log(x)}\, dx}[/tex]

    I know I would need to get the limit from n to infinity and swap infinity in the integral with n.
    I don't know what to do with (1/(xlnx))dx . I cant do by sums and wen I do by parts I cant find dv which I set to ln(x)^(-1)dx. Im just not sure where to go with this...
    substitute:

    u = log(x)
    Last edited by stapel; 10-26-2014 at 08:50 AM. Reason: Copying typed-out text into reply.
    “... mathematics is only the art of saying the same thing in different words” - B. Russell

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