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Integral error

  1. Feb 12, 2014 #1

    Radarithm

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    1. The problem statement, all variables and given/known data

    Evaluate: [tex]\int{xe^{ax}}dx[/tex]

    2. Relevant equations

    Integration by substitution

    3. The attempt at a solution

    I'm on a phone at the moment. My work: http://postimg.org/image/v4hdr5uqx/ [Broken]

    The correct answer was:
    [tex]\frac{xe^{ax}}{a}-\frac{e^{ax}}{a^2}[/tex]
     
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Feb 12, 2014 #2

    SteamKing

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    You should do this integral by parts. Some of your original substitutions don't look OK.
     
  4. Feb 12, 2014 #3

    Radarithm

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    http://postimg.org/image/ao3mi4ygz/ [Broken]

    I feel like I'm getting closer but I'm still making a dumb mistake. Is it with the derivatives?
     
    Last edited by a moderator: May 6, 2017
  5. Feb 12, 2014 #4

    eumyang

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    If [itex]dv = e^{ax} dx[/itex], then [itex]v = e^{ax}[/itex] is wrong. There are also multiple errors on the second line, but you need to fix what I said first.
     
  6. Feb 13, 2014 #5

    Radarithm

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    Got it. Thanks for pointing out my mistakes.
    [tex]\int{xe^{ax}}dx[/tex] [tex] u=x du=dx dv=e^{ax}dx v=\frac{e^{ax}}{a} [/tex]
    [tex]\frac{xe^{ax}}{a}-\int{\frac{e^{ax}}{a}}dx[/tex]
    [tex]\frac{xe^{ax}}{a}-\int{e^{ax}a^{-1}}dx=\frac{xe^{ax}}{a}-\frac{e^{ax}}{a^2}[/tex]

    Power rule + derivative mistake
    Thanks for the help.
     
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