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Integration of 3 lnx/x

  1. Mar 3, 2008 #1
    Can anybody help me out with this?

    3lnx/x du = ( ? ) dx. What is the question mark? Leave no spaces in your answer.

    I thought u was 3lnx, which would be make it 3/x dx. Apparently not. Can anybody show me the right way of doing this sort of problem please?
     
  2. jcsd
  3. Mar 3, 2008 #2
    Are you trying to solve for u? If so:

    (x/3lnx)dx = du

    You can integrate both sides, the left by integration by parts, I think will work.
     
  4. Mar 3, 2008 #3

    HallsofIvy

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    That really makes no sense without knowing how u depends on x. Why did you "think u was 3ln(x)"? Are you leaving out part of the problem?
     
  5. Mar 3, 2008 #4
    Sorry, I should have been more clear. I just copied and pasted the problem. The question was 3lnx/x, and I just needed to find the first part of the problem. The professor wanted us to "find u, and take it one more step." I thought that step was differentiating u. All I really need is what would be in the brackets with respect to dx.
     
  6. Mar 3, 2008 #5

    HallsofIvy

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    Then knowing that the derivative of ln(x)= 1/x should help you! 3ln(x)/x dx= 3(ln x)(dx/x). I would incline toward setting u= ln x. What is du now?
     
  7. Mar 3, 2008 #6
  8. Mar 4, 2008 #7
    should be 1/x dx precise.
     
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