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Homework Help: Simple Indefinite Integral

  1. May 28, 2010 #1
    [tex]\int\frac{4}{-e^{4x-7}}[/tex]

    [tex]=ln-e^{4x-7}}[/tex]

    [tex]=-4x+7+C[/tex]

    The answer says it is:

    [tex]=\-e^{-4x+7}+C[/tex]
     
    Last edited: May 28, 2010
  2. jcsd
  3. May 28, 2010 #2

    D H

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    The book is right, which is easily verifiable by computing the derivative the given answer.
     
  4. May 28, 2010 #3
    Is there somewhere I went wrong? I am guessing it has something to do with the ln.
    I thought that

    [tex]\ln{e}=1[/tex]

    Therefore: [tex]ln-e^{4x-7}}=-4x+7+C[/tex]
     
    Last edited: May 28, 2010
  5. May 28, 2010 #4

    D H

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    Yes, the problem is with the natural logarithm.

    Just because [itex]\int \frac 1 x \,dx = \ln x[/itex] does not mean that everything of the form [itex]\int \frac 1{f(x)}\,dx[/itex] integrates to [itex]\ln(f(x))[/itex].
     
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