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Math Help - integration by parts

  1. #1
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    integration by parts

    1)  \int xe^{2x}dx

    u = x,  dv = e^{2x}dx
    du = dx, v = e^{2x}

    \int udv = uv-\int vdu

     xe^{2x}-\int e^{2x}dx

    xe^{2x}-e^{2x}+C

    what i got is wrong, i think im doing something wrong with e^{2x}
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  2. #2
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    Quote Originally Posted by viet View Post
    1)  \int xe^{2x}dx
    Let u=x \mbox{ and }v' = e^{2x}\Rightarrow u' = 1 \mbox{ and } v= \frac{1}{2}e^{2x}

    Thus,
    \int u v' dx = uv - \int u'v dx
    And hence,
    \int xe^{2x} dx = \frac{1}{2}xe^{2x} - \int \frac{1}{2} e^{2x} dx = \frac{1}{2}xe^{2x} - \frac{1}{4}e^{2x}+C
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  3. #3
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    Hello, viet!

    I think im doing something wrong with e^{2x} . Yes!
    \int e^{2x}dx \:=\:\frac{1}{2}\,e^{2x} + C
    . . . . . . . . \uparrow

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