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Help with this integral

  1. Oct 13, 2006 #1
    [tex]\int \frac{1}{x\log_{e} 4x} dx


    wow i finally got latex to work

    ok... so i did it on a text and got [tex]\log_{e}(\log_{e}4x)+c[/tex]

    now i did it and got [tex]\frac{1}{4}\log_{e}(\log_{e}4x)+c[/tex]

    which is right?

    what is the derivative of [tex]\log_{e}4x[/tex] ?
    Last edited: Oct 13, 2006
  2. jcsd
  3. Oct 13, 2006 #2
    do you mean [tex] \int \frac{1}{x\ln 4x} dx [/tex]? Use the substitution [tex] u = \ln 4x [/tex].
  4. Oct 13, 2006 #3
    your first answer is correct. can you see why?

    [tex] \log_{e} 4x = \ln 4x [/tex]. Can you take the derivative of that now?
  5. Oct 13, 2006 #4

    ohhhh.... is it [tex]\frac{4}{4x} = \frac{1}{x} [/tex] ?
  6. Oct 13, 2006 #5
    yes it is.
  7. Oct 13, 2006 #6
    i see.. Thanks
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