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Integration problem

  1. Nov 9, 2004 #1
    can anyone solve this equation?

    ∫x^3/(x^2+1)^(3/2) dx
     
  2. jcsd
  3. Nov 9, 2004 #2
    [tex]\int\frac{x^3}{\left(x^2+1\right)^{\frac{3}{2}}}dx=\frac{x^2+2}{\sqrt{x^2+1}}+C[/tex]
     
  4. Nov 9, 2004 #3

    Galileo

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    Hmm, maybe integration by parts would work?
    [tex]\frac{x^3}{\left(x^2+1\right)^{\frac{3}{2}}}=x^2\frac{x}{\left(x^2+1\right)^{\frac{3}{2}}}[/tex]
    The primitive of the factor on the right is
    [tex]\frac{-1}{\sqrt{x^2+1}}[/tex]
    looks like it may lead somewhere.
    Appears tedious though
     
    Last edited: Nov 9, 2004
  5. Nov 9, 2004 #4
    :surprised
     
  6. Nov 9, 2004 #5

    dextercioby

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    Proof
    [tex]\int\frac{x^3}{\left(x^2+1\right)^{\frac{3}{2}}}dx=
    \int\frac{x^2}{2}\frac{2x}{(\sqrt{x^2+1})^3}dx=
    -\frac{x^2}{\sqrt{x^2+1}}+\int\frac{2x}{\sqrt{x^2+1}}dx=
    -\frac{x^2}{\sqrt{x^2+1}}+2\sqrt{x^2+1}+C=
    \frac{x^2+2}{\sqrt{x^2+1}}+C[/tex]
     
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