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Integration problem

  1. Sep 30, 2007 #1
    1. The problem statement, all variables and given/known data
    Integrate x^3*sqrt(x^2 +1)

    2. Relevant equations
    The problem is to be solved by using substitution

    3. The attempt at a solution
    To be honest i'm at a complete stump here, I've tried most values for U. My first guess was x^3, since du/dx = 3x^2, but I can't substitute this into a root, can I? Choosing x^2+1 as U is also moot, as the derivative equals 2x and by substituting you are still left with x^2 on the left side of the equation.

    So I thought perhaps the best idea would be to substitute all of sqrt(x^2 +1), as the derivative becomes x/(sqrt(x^2+1)) = x/u, but even then, i'm stuck with x^2 by substituting.

    I've also tried all sorts of ways to rewrite the equation (such as x^3*(x^2+1)^0.5, however, with no luck). I'm really starting to wonder how i'm supposed to integrate this function by use of substitution, anyone got any thoughts that could push me in the right direction?

  2. jcsd
  3. Sep 30, 2007 #2
    Ah, but x^2 = u-1.
  4. Sep 30, 2007 #3
    Aah of course, thank you for the help, my man. Seeing those little things is what makes integration fun, except of course, when you don't see them ;p.

    Thanks again!
  5. Sep 30, 2007 #4


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    Have you considered writing [itex]x^3\sqt{x^2+ 1}[/itex] as [itex]x^2\sqrt{x^2+1} (x)[/itex] and letting u= x2[/sup[+ 1?
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