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How do I do this integration using u sub?

  1. Jun 9, 2014 #1
    1. The problem statement, all variables and given/known data
    ∫x^2√(2+x)

    using u sub


    2. Relevant equations
    ∫x^2√(2+x)


    3. The attempt at a solution

    I can't seem to find anything to use for a u sub.

    if I sub 2+x I just get 1, and if I sub x^2 I just get 2x

    If I do √(2+x) I just get 1/2(1/√(2+x))
     
  2. jcsd
  3. Jun 9, 2014 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Frankly, I really don't know what you mean by
    "if I sub 2+x I just get 1, and if I sub x^2 I just get 2x
    If I do √(2+x) I just get 1/2(1/√(2+x)) "

    You get 1 for what? The integral? Show your work! HOW did you get "1"?
     
  4. Jun 9, 2014 #3

    benorin

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    Homework Helper

    Let [itex]J:=\int x^2\sqrt{x+1}dx[/itex]. Put [itex]u=x+1\Rightarrow du=dx[/itex] to get [itex]J=\int (u-1)^2\sqrt{u}du=\int \left( u^\frac{5}{2}-2u^\frac{3}{2}+u^\frac{1}{2}\right) du[/itex]
     
  5. Jun 9, 2014 #4
    The derivative of 2+x = 1
     
  6. Jun 9, 2014 #5
    Thanks, so I use change of variable to get my answers, I should've seen that.
     
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