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Integration help

  1. Aug 11, 2012 #1
    1. The problem statement, all variables and given/known data

    find

    2. Relevant equations

    [tex]\int log\sqrt{1+x^2}dx[/tex]

    3. The attempt at a solution

    I honestly don't know what to do?
     
  2. jcsd
  3. Aug 11, 2012 #2

    dextercioby

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    I would use a hyperbolic function to make a substitution to get rid of the square root.
     
  4. Aug 11, 2012 #3
    I don't know how to do that?
     
  5. Aug 11, 2012 #4

    dextercioby

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    [tex] x = \sinh t [/tex] would be the obvious candidate.
     
  6. Aug 11, 2012 #5
    So is that a substitution?
     
  7. Aug 11, 2012 #6
    the answer is xlnx-x+c is that right?
     
  8. Aug 11, 2012 #7

    dextercioby

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    You'll have to make the calculations on your own. I just gave you a point to start from, assuming you have knowledge of hyperbolic functions. Another option is to use integration by parts.
     
  9. Aug 11, 2012 #8
    Yes, hyperbolic substitution would work here.
     
  10. Aug 11, 2012 #9
    Hello mill
    but is the answer xlnx-x
    also, is the derivative of ln(x^2) just 2/x and the derivative of (lnx)^2 is 2lnx/x ?
     
  11. Aug 11, 2012 #10
    Xtreme, why don't you try differentiating your answer to check whether if it is correct?
    And answering your question about derivatives: Yes, they are both correct.
     
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