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Math Help - Integral - Show me the steps?

  1. #1
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    Integral - Show me the steps?

    Hello,

    The problem I'm working on is:

    The integral of: (x^2 + 2)/(x+1)^2

    Can you please step me through this problem?

    Thanks!
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  2. #2
    MHF Contributor MarkFL's Avatar
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    Re: Integral - Show me the steps?

    I would manipulate the integrand as follows:

    \frac{x^2+2}{(x+1)^2}=\frac{x^2+2x+1-2x+1}{(x+1)^2}=\frac{(x+1)^2-2x+1}{(x+1)^2}=1-\frac{2x-1}{(x+1)^2}=

    1-\frac{2x+2-3}{(x+1)^2}=1-\frac{2(x+1)-3}{(x+1)^2}=1-\frac{2}{x+1}+\frac{3}{(x+1)^2}

    Now, integrate term by term.
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