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Thread: how to integrate this??

  1. #1
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    how to integrate this??

    im trying to integrate the function $\displaystyle x(1-x)$ which is $\displaystyle x-x^2$. if I make u=x^2 or u=x-x^2 for u-substitution it never turns out right though.. please someone help
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Arez View Post
    im trying to integrate the function $\displaystyle x(1-x)$ which is $\displaystyle x-x^2$. if I make u=x^2 or u=x-x^2 for u-substitution it never turns out right though.. please someone help
    u-substitution?! this is power rule!

    remember, $\displaystyle \int x^n ~dx = \frac {x^{n + 1}}{n + 1} + C$ ........(for any constant $\displaystyle n \ne -1 $ of course )

    here you have $\displaystyle \int x^1~dx - \int x^2~dx$, just integrate each separately using the power rule
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  3. #3
    Moo
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    Hello,

    No, don't substitute anything

    $\displaystyle \int x-x^2 ~dx=\int x ~dx-\int x^2 ~dx$

    Then recall this common antiderivative :
    $\displaystyle \int x^n ~ dx=\frac{x^{n+1}}{n+1}+C$, for any $\displaystyle n \neq 1$



    Edit : woops, too late
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