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Math Help - integrate

  1. #1
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    integrate

     \frac{1}{2}xe^{\frac{-x}{2}}

    i used parts and wondering wether im correct.thats to the power of -x/2 (its a bit small)!
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  2. #2
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    Quote Originally Posted by skystar View Post
     \frac{1}{2}xe^{\frac{-x}{2}}

    i used parts and wondering wether im correct.thats to the power of -x/2 (its a bit small)!
    That would probably be the easiest way to integrate it. Sub in u = x/2 first, though.

    -Dan
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  3. #3
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    I get

    <br />
\int \frac{1}{2} x e^{- \frac{x}{2}} dx = -e^{-\frac{x}{2}}(x+2)
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  4. #4
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    i got different nooooo!
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  5. #5
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    can someone show me how im such an idiot
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  6. #6
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    Quote Originally Posted by skystar View Post
    can someone show me how im such an idiot
    Show all your working and your mistake(s) will be pointed out.
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  7. #7
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    ok first of all substutute u=\frac{x}{2}

    therefore x=2u and du=\frac{1}{2}dx

    so we have
    2 \int u e^{-u} du

    using parts once we have

    2(-ue^{-u}+\int e^{-u} du)

    2(-ue^{-u}-e^{-u})+c

    -2e^{-u}(u+1)+c

    -2e^{-\frac{x}{2}}(\frac{x}{2}+1)+c

    -2e^{-\frac{x}{2}}(\frac{x+2}{2})+c

    -e^{-\frac{x}{2}}(x+2)+c
    Last edited by thelostchild; June 2nd 2008 at 12:09 PM.
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