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Integration by parts involving exponentials and logarithms

  1. Nov 18, 2009 #1
    1. The problem statement, all variables and given/known data

    Using integration by parts, integrate:
    (1/x^2)(lnx) dx with the limits e and 1


    2. Relevant equations

    [uv]to the limits a b - the integral of (v)(du/dx) dx

    (sorry, dont know how to write out equations properly on a computer)

    3. The attempt at a solution

    I've got u=x^-2 so du/dx= -2x^-3
    dv/dx=lnx so v= x(lnx-1)

    So putting this into the equation above:
    [x^-2.x(lnx-1)] - the integral of (-2x^-3.x(lnx-1))

    Is this right so far?
    If so how do I integrate the last part? Do I do it sepeartley or by parts again?

    Many Thanks, any help at all would be greatly appreciated.
     
  2. jcsd
  3. Nov 18, 2009 #2

    tiny-tim

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    Hi xllx! :smile:

    (have an integral: ∫ and try using the X2 tag just above the Reply box :wink:)
    eugh! :yuck:

    go the other way …

    integrate x-2 ! :smile:
     
  4. Nov 18, 2009 #3
    Thankyou. Redid it and came out with a reasonal answer.
     
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