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Homework Help: Tricky Integration

  1. Dec 5, 2017 #1
    1. The problem statement, all variables and given/known data
    How do I solve ##\frac{20\ln{(t)}}{t}##???

    2. Relevant equations


    3. The attempt at a solution
    Is it easier to calculate this without integrating by parts???
    I'm not sure where to start.
     
  2. jcsd
  3. Dec 5, 2017 #2

    andrewkirk

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    Solving by integration by parts is easy - very few lines. I can't think of an easier way.
     
  4. Dec 5, 2017 #3
    There is an easier way. Try a simple "u-substitution".
     
  5. Dec 5, 2017 #4

    fresh_42

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    You have ##f\cdot f'## which is half of ##(f^2)'##. Done.
     
  6. Dec 5, 2017 #5
    I like the simplicity, but shouldn't it be just half of ##(f^2)## ?

    edited: forgot the "half of"
     
  7. Dec 5, 2017 #6

    fresh_42

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    ##f^2## is the solution after integration, but I said ##f \cdot f' = \frac{1}{2} \cdot (f^2)'## for the integrand. Of course this all is a bit sloppy: no integration boundaries or the constant, no mentioning of ##\ln |x|## in the OP and no ##dt 's##.
     
  8. Dec 5, 2017 #7
    Agreed. Thanks for clearing that up.
     
  9. Dec 6, 2017 #8

    Math_QED

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    Substitute ##u = \ln t, du = \frac {1}{t}dt##
     
  10. Dec 6, 2017 #9
    Thanks everyone. The solution is ##10\ln{(t)}^2##.
     
  11. Dec 7, 2017 #10

    SammyS

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    You might like to remove an ambiguity.

    Is that the natural log of the square of t, or is it the square of the natural log of t ?

    Also, I suspect that you need to include a constant of integration .
     
  12. Dec 7, 2017 #11
    Typically for integrals involving ln in a typical calculus course...

    Always try u sub. If that does not work, then integration by parts. Keep this in mind.
     
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