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Homework Help: Take the anti derivative of (X^2)/sqrt(1-x)soln' . let u=1-x

  1. Jan 11, 2006 #1
    take the anti derivative of (X^2)/sqrt(1-x)

    soln'.... let u=1-x... then -du=dx and x^2 = (1-u)^2 (sub back in)...

    this gives me -2*u^(1/2)*(15-10*u+3*u^2) /15.... (sorry for lack of proper terms)


    anyway, this turns out to be wrong...where did i go wrong here?
     
  2. jcsd
  3. Jan 11, 2006 #2

    benorin

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    Homework Helper

    Try this:

    [tex]\int \frac{x^2}{\sqrt{1-x}}dx = -\int \frac{(1-u)^2}{\sqrt{u}}du = -\int u^{-\frac{1}{2}}(1-2u+u^2) du[/tex]

    then distribute the [itex]u^{-\frac{1}{2}}[/itex] term over the quadratic and integrate
     
  4. Jan 11, 2006 #3
    yeah...that's what i was getting but it was in a different form. Thanks a lot !!1
     
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