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Help solve this integral (by parts possibly)

  1. Aug 6, 2015 #1
    QUESTION:

    The question is to find the improper integral of (x^1/2)/lnx dx.

    MY ATTEMPT:
    1)I tried it byparts, by taking 1/ln x as 'u' or the first function but i got stuck.

    2)Alternatively, I tried substituting x=e^2t in hopes to eliminate ln for a simpler byparts integration, but that didn't work
    out.

    Please help asap. Thanks.
     
  2. jcsd
  3. Aug 6, 2015 #2
    You can apply parts directly. Apply parts in the form such that the evaluation of the new integral involves the derivative of (1/lnx).
     
  4. Aug 6, 2015 #3
    I tried it this way. The furthest I got was

    (2*(x)^(1/2))/lnx - Integral of (2/((x)^(1/2))(lnx)^2 dx

    Still not able to attain the answer.
     
  5. Aug 6, 2015 #4
    I believe this to be the way to approach. Then the evaluation of the new integral is straightforward.

    <Mod note: attachment deleted>
     
    Last edited by a moderator: Aug 6, 2015
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