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Integral + brainfart

  1. Aug 4, 2009 #1
    Hai,

    I have the following Integral i can't get right:
    [tex]\int_{-8}^8\frac{(6e^{4x}-2)^2}{e^{4x}}[/tex]

    After i squared the bracket i end up with[tex]~~\frac{36e^{8x}-24e^{8x}+4}{e^{4x}}[/tex]

    So, after dividing thru by [tex]e^{4x}[/tex] i have:

    [tex]36e^{4x}-24e^{4x}+\frac{4}{e^{4x}}[/tex]

    Integrating gives:
    [tex]9e^{4x} - 6e^{4x} +4~ln(e^{4x})[/tex]

    I must be doing something wrong because i end up with the wrong answer =/
    But what?
     
  2. jcsd
  3. Aug 4, 2009 #2

    zcd

    User Avatar

    [tex]\int 36e^{4x}-24e^{4x}+\frac{4}{e^{4x}}\,dx=\int 36e^{4x}-24e^{4x}+4e^{-4x}}\,dx[/tex]
    You skipped the u substitution for the last term.
     
  4. Aug 4, 2009 #3

    rl.bhat

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    Homework Helper

    The third integration becomes
    Int(4*e^-4x) = - e^-4x.
     
  5. Aug 4, 2009 #4

    Pengwuino

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    Gold Member

    The second term in line 2 should be [tex] - 24e^{4x} [/tex]. Also, the integral of [tex]4e^{ - 4x} [/tex] is not [tex]4\ln (e^{4x} )[/tex]
     
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