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Homework Help: Calculational Integral

  1. Oct 7, 2007 #1
    1. The problem statement, all variables and given/known data

    [tex]\int\frac{x^3dx}{\sqrt{2-x}}[/tex]




    3. The attempt at a solution
    I solved it in this way
    for v=2-x
    [tex]\int-\frac{(2-v)^3dv}{\sqrt{v}}=-\int\frac{(8-12v+6v^2+v^3)dv}{\sqrt{v}}
    =-\int\frac{8dv}{\sqrt{v}}+\int 12\sqrt{v}dv-\int 6v\sqrt{v}dv-\int v^2\sqrt{v}dv[/tex]
    is it true?
    Is there any other methods?
     
    Last edited: Oct 7, 2007
  2. jcsd
  3. Oct 7, 2007 #2
    That's one way of doing it. If you substitute v2 for 2-x, you will have a radical-free expression to integrate.
     
  4. Oct 7, 2007 #3
    Ok,very nice.
     
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