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Math Help - What's wrong with that integral

  1. #1
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    What's wrong with that integral

    \int xe^{-x} dx
    u=x
    du=dx
    v=e^x
    dv=e^{-x}dx
    \int xe^{-x} dx=xe^{-x} - \int e^{-x} dx = xe^{-x}-e^{-x}+C
    mathbook gives: -xe^{-x}-e^{-x}+C
    where does that minus come from ?
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  2. #2
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by totalnewbie View Post
    \int xe^{-x} dx
    u=x
    du=dx
    v=e^x
    dv=e^{-x}dx
    \int xe^{-x} dx=xe^{-x} - \int e^{-x} dx = xe^{-x}-e^{-x}+C
    mathbook gives: -xe^{-x}-e^{-x}+C
    where does that minus come from ?
    You essentially got it right, just (I assume) two small typos that screwed you up.

    dv=e^{-x}dx so v=-e^{-x}.

    Make the new substitution and everything will work out.

    Your second typo was here:
    \int xe^{-x} dx = xe^{-x} - e^{-x}+C

    According to your work, the sign of the e^{-x} term should have been a "+", which is why you got the sign of that term correct.

    -Dan
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