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X((2x^2) - 2)^3 antiderivative

  1. Nov 24, 2004 #1
    how do I find to antiderivative of:

    x((2x^2) - 2)^3
     
  2. jcsd
  3. Nov 24, 2004 #2

    ehild

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    x(2x^2-2)^3=8x(x^2-1). Replace x^2-1 by t, notice that dt=2dx, so

    [tex]\int x(2x^2-2)^3dx=\int 4 t^3 dt [/tex]

    then replace back

    [tex]t=x^2-1[/tex]

    ehild
     
    Last edited: Nov 25, 2004
  4. Nov 24, 2004 #3
    from there I was suppose to compute as x is goes from 0 to 1
    I got 0, but the answer is -1
     
  5. Nov 25, 2004 #4

    ehild

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    There was a typo in my message. It is

    [tex]\int x(2x^2-2)^3dx=\int 4 t^3 dt [/tex]

    correctly, which is t^4= (x^2-1)^4.

    [tex] \big[(x^2-1)^4\big]_0^1=(1-1)^4-(0-1)^4=-1[/tex]

    ehild
     
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