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Homework Help: Integral of x^2/(x+2)

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    Evaluate the integral:
    [itex]\int \frac{x^2}{x + 2} dx[/itex]

    2. Relevant equations

    There aren't any relevant equations...

    3. The attempt at a solution

    In these type of problems you have to set [itex]u = \text{something}[/itex] so I tried setting [itex]u = x^2[/itex], but then [itex]\text{du} = 2x\text{dx}[/itex] and you can't substitute anything. And if [itex]u = x + 2[/itex] then [itex]\text{du} = 1[/itex] and that's useless.

    Also, this problem is from the Swokowski calculus textbook (school starts in two days for me so I'm doing self study :smile: )
    Last edited: Aug 23, 2011
  2. jcsd
  3. Aug 23, 2011 #2


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    Homework Helper

    Before you do anything, do polynomial division (degree of top >= degree of bottom). Once this is done, it should be trivial to take the integral.
  4. Aug 23, 2011 #3
    Try doing some algebra first. You can rewrite that. Polynomial long division.
  5. Aug 23, 2011 #4


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    Staff Emeritus
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    Homework Helper

    In you second substitution, where u = x+2, du = dx not du = 1

    If you carry thru with this substitution properly, you can find the desired integral.
  6. Aug 23, 2011 #5
    Wow, I can't believe I missed that. Here's what I have from there:

    Clearly [itex]\frac{x^2}{x + 2} = x - 2 + \frac{4}{x + 2}[/itex]. So integrating that we have [itex]\frac{x^2}{2} - 2x + 4\ln{|x+2|} + C[/itex] where C is a constant.

    Thanks for your help guys! I appreciated it :smile:

    Also, to SteamKing, yes, I made a mistake while typing it up.
    Last edited: Aug 23, 2011
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