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Math Help - Question to Calculus Tutorial

  1. #1
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    Question to Calculus Tutorial

    - hello again

    im working my way thourgh the awesome calculus tutorial but now im stuck at one point:

    \int x^2 e^x<br />
    Last edited by mr fantastic; June 7th 2009 at 06:51 PM. Reason: Restored question deleted by OP
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by coobe View Post
    hello again

    im working my way thourgh the awesome calculus tutorial but now im stuck at one point:

    \int x^2 e^x<br />
    You will need integration by parts twice

    The first time gives

    \int x^2 e^xdx=x^2e^x-2\int xe^xdx

    and the 2nd is

    \int x^2 e^xdx=x^2e^x-2(xe^x-\int e^xdx)

    So finally you get

    \int x^2 e^xdx=x^2e^x-2xe^x+2e^x +C
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  3. #3
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    Question to Calculus Tutorial

    \int x^2 e^x
    \\u = x^2\\
    \\v'=e^x\\
    \\u'=2x\\
    \\v =e^x\\
    \\x^2e^x-\int 2xe^xdx = x^2 e^x -2\int x e^x

    everything clear so far. but now it seems the author is missing an e^x
    the given solution: x^2-2xe^x+2e^x+C

    is it just a typo or am i missing something ?
    Last edited by mr fantastic; June 7th 2009 at 06:51 PM. Reason: Moved from another thread.
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  4. #4
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    You're right. It should've been:
    x^2e^x - 2xe^x + 2e^x + C

    You can always to differentiate your answer and see if you get your original integrand. That way you can make sure if you got it right or not.
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  5. #5
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    Quote Originally Posted by coobe View Post
    hello again

    im working my way thourgh the awesome calculus tutorial but now im stuck at one point:

    \int x^2 e^x
    \\u = x^2\\
    \\v'=e^x\\
    \\u'=2x\\
    \\v =e^x\\
    \\x^2e^x-\int 2xe^xdx = x^2 e^x -2\int x e^x

    everything clear so far. but now it seems the author is missing an e^x
    the given solution: x^2-2xe^x+2e^x+C

    is it just a typo or am i missing something ?
    You haven't finished. Integrate \int x e^x dx by using "integration by parts" again.
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