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Math Help - integral of (x+3)e^-x by parts

  1. #1
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    Question integral of (x+3)e^-x by parts

    Question is to integrate the following integral by parts

    <br />
\int {(x + 3)e^{ - x} dx} <br />

    Is this right?

    <br />
\begin{array}{l}<br />
 u = x + 3 \\ <br />
 u' = 1 \\ <br />
 v' = e^{ - x}  \\ <br />
 v =  - e^{ - x}  \\ <br />
 \int {(x + 3)e^{ - x} dx}  \\ <br />
  = (x + 3) \times  - e^{ - x}  - \int {1 \times  - e^{ - x} dx}  \\ <br />
  =  - (x + 3)e^{ - x}  - e^{ - x} +K \\ <br />
 \end{array}<br />


    The answer is given as

    <br />
 - e^{ - x} (x + 4) + K<br />
    but I can't see how
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  2. #2
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    Smile

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  4. #4
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    Arrow

    Sorry, was I right in my answer?
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  5. #5
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    all its right, but you didn't finish your answer
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  6. #6
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    how do you mean I didn't finish my answer?
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  7. #7
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    Quote Originally Posted by Craka View Post
    how do you mean I didn't finish my answer?
    = - (x + 3)e^{ - x} - e^{ - x} + K = -x e^{-x} - 3e^{-x} - e^{-x} + K = -xe^{-x} - 4 e^{-x} + K = -e^{-x} (x + 4) + K.
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  8. #8
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    whoops. Thanks.
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