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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- Apr 5th 2009, 12:54 PMArezhow 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

- Apr 5th 2009, 12:58 PMJhevon
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 :D)

here you have $\displaystyle \int x^1~dx - \int x^2~dx$, just integrate each separately using the power rule - Apr 5th 2009, 12:58 PMMoo
Hello,

No, don't substitute anything (Surprised)

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

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