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Math Help - Using u-substitution, integrate ∫(x^3)(x^2-1)^(3/2)dx

  1. #1
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    Post Using u-substitution, integrate ∫(x^3)(x^2-1)^(3/2)dx

    ∫(x^3)(x^2-1)^(3/2)dx

    I tried u=x^2 - 1, but then I get (1/2)du=xdx, and I have an x^3, so that's not working...what should I do?
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  2. #2
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    On the contrary, u = x^2 - 1 is an ideal substitution.

    du = 2x~dx yields

    \int (x^2)(x^2-1)^{\frac{3}{2}}~du = \int (u+1)u^{\frac{3}{2}}~du

    Do you see why?
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  3. #3
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    It's x^3 though, not x^2
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  4. #4
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    \frac{x^3}{2x} = \frac{1}{2}x^2

    I forgot to put the constant in my previous post.
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