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How to integrate int sin(ln(x)) ?

  1. Jun 15, 2009 #1
    1. The problem statement, all variables and given/known data

    I am having trouble solving the following:

    [tex]\int[/tex]sin(lnx) dx


    3. The attempt at a solution

    I let u = ln x but this makes xdu = dx so I am left with

    [tex]\int[/tex]x sinu du
     
  2. jcsd
  3. Jun 15, 2009 #2

    Cyosis

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    Re: Integration

    That's the substitution you want to use,but you can't leave the x in there. If u=lnx, then x is?
     
  4. Jun 15, 2009 #3
    Re: Integration

    Would x = u2?

    [tex]\int[/tex]ue sin u du

    Then do you do it by parts or something?
     
  5. Jun 15, 2009 #4

    Cyosis

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    Re: Integration

    How on earth did you get that? Can you solve [itex]u=\ln x[/itex] for x?
     
  6. Jun 15, 2009 #5
    Re: Integration

    Oops I meant e^u, is that right?
     
  7. Jun 15, 2009 #6

    Cyosis

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    Re: Integration

    Yes that's correct. You can now use integration by parts, twice.
     
  8. Jun 15, 2009 #7
    Re: Integration

    does e(lnx) cancel to 1?
     
  9. Jun 15, 2009 #8

    Cyosis

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    Re: Integration

    No and you should really know that at this stage! If a function has an inverse, [itex]f^{-1}(x)[/itex], then [itex]f^{-1}(f(x))=f(f^{-1}(x))=x[/itex]. So what is [itex]e^{\ln x}[/itex] and [itex]\ln e^x[/itex]?
     
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