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Not sure how to proceed with uv-vdu integral

  1. Jun 19, 2011 #1
    hi, im trying to find the integral of x^3sqrt(1+x^4)dx
    i set it up like this:

    u=x^3 dv=sqrt(1+x^4)
    du = 3x^2dx v=2/3(1+x^4)^(3/2)

    and using uv-integralvdu i get

    (2/3x^3(1+x^4)^3/2) - 2/3integral((1+x^4)^(3/2)3x^2)dx

    i know that in the end, the integral should equal 1/6(x^4+1)^(3/2) but i dont know how to get there from where i stopped...

  2. jcsd
  3. Jun 19, 2011 #2


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    Integration by parts is not the best way to do this integral. Try a simple u-substitution:

    u = 1 + x4.
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