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Integration of the natural log

  1. Oct 10, 2012 #1
    1. how to integrate∫ (ln x)2 /x dx



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Oct 10, 2012 #2
    Here it is better to show what you have attempted so far, after all people here are not answer machine. But a hint can be: what is the derivative of ln x?
     
  4. Oct 10, 2012 #3

    SammyS

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    Although, raopeng suggests that you show what you've attempted, it is actually a part of the rules for posting a thread in the homework help section of this Forum.


    raopeng's hint is excellent.
     
  5. Oct 10, 2012 #4
    x(ln x)-1+c..i not pretty sure..
     
  6. Oct 10, 2012 #5

    SammyS

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    The derivative of ln(x) is (1/x) + C .

    Do you know integration by substitution?
     
  7. Oct 10, 2012 #6
    i know..let u= ln x
    then differenciate du/dx= 1/x..
     
  8. Oct 10, 2012 #7
    i know..let u= ln x
    then differenciate du/dx= 1/x..
     
  9. Oct 10, 2012 #8

    SammyS

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    After doing all that, what does your integral become, in terms of u ?
     
  10. Oct 10, 2012 #9
    u^2 du..right.?
     
  11. Oct 10, 2012 #10
    let u= ln x
    du/dx= 1/x
    dx= x du..
    then integrate (u^2/x) x du
    then cancel the x...so, integrate the u^2..
    right.? i got the idea..tq..
     
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