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Math Help - Integral Indefine

  1. #1
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    Integral Indefine

    \int{x(2-x^2)^3}\,dx



    How could I get the -1/2???
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  2. #2
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    Quote Originally Posted by dianjoey View Post
    \int{x(2-x^2)^3}\,dx



    How could I get the -1/2???
    I think what you want is
     <br />
\int x(2-x^2)^3\,dx = -\frac{1}{2}\int (2-x^2)^3\, d(2-x^2)<br />

    but it's really better if you use a substitution. Let u = 2-x^2 (the hard part of this). Then du = -2 x \,dx so x\,dx = -\frac{1}{2}\,du so the original problem becomes

     <br />
-\frac{1}{2} \int u^3\,du<br />
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  3. #3
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    Hi Danny,

    I was asking where the -\frac 12\ come from...
    I don't know how to get that...
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