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Math Help - [SOLVED] Quick Question

  1. #1
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    [SOLVED] Quick Question

    I'm having problems with this question ...
    What is the integral of x/(x+2) with respect to x.

    A) x ln|x+2| + C
    B) x + 2 ln|x+2| + C
    C) x - 2 ln|x+2| + C
    D) x - ln|x+2| + C
    E) X - Arctan x + C

    I know the integral of 1/(x+2) is ln|x+2|, but I don't know how to deal with the x in the numerator.

    Thanks
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  2. #2
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    \frac{x}{x+2} = \frac{x+2-2}{x+2} = \frac{x+2}{x+2} - \frac{2}{x+2} = 1 - \frac{2}{x+2}

    now integrate
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  3. #3
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    oh wow, thanks. I never thought it that way.
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  4. #4
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    you can also use long division ... it's just more difficult to format in a post.
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