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Homework Help: Integration by parts problem

  1. Nov 12, 2006 #1
    "Evaluate the integral [0,1] x^3/sqrt[x^2 + 1] by integration by parts"

    I know I have to use the integration by parts equation, but I don't know what to make u and what to make dv..
  2. jcsd
  3. Nov 12, 2006 #2


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    Try rewriting the integral thus;

    [tex]\int^{1}_{0}\; \frac{x^{3}}{\sqrt{x^2+1}} \; dx = \int^{1}_{0}\; x^3 (x^2 +1)^{-\frac{1}{2}} \;dx[/tex]

    Now, to determine which term to make u and dv, think about which one will simplify your expression most when you differentiated it and set this to u.
  4. Nov 12, 2006 #3
    You could start by rewriting the integrand:

    \frac{x^3}{\sqrt{x^2+1}}=x^3 (x^2+1)^{-1/2} = [x^{-6} (x^2+1)]^{-1/2}

    And the apply the integration by parts formula. That should make it easier.
  5. Nov 12, 2006 #4
    OH okay, thank you!
  6. Nov 12, 2006 #5
    Do you have to do it by parts? Much easier to substitute [tex]u = x^2 [/tex]
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