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Math Help - Antiderivative Example

  1. #1
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    Antiderivative Example

    Hello,
    I was doing the antiderivative of:

    f'(x) = (x^2-1)/x

    Am I allowed to separate this into x^2/x - 1/x? Or do the brackets prevent me from doing so?

    If not, how do I approach this antiderivative? Thanks for anyone's help!
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  2. #2
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    Quote Originally Posted by ty2391 View Post
    Hello,
    I was doing the antiderivative of:

    f'(x) = (x^2-1)/x

    Am I allowed to separate this into x^2/x - 1/x? Or do the brackets prevent me from doing so?

    If not, how do I approach this antiderivative? Thanks for anyone's help!
    you have the correct approach ... \frac{x^2-1}{x} = x - \frac{1}{x}

    antiderivative is \frac{x^2}{2} - \ln|x| + C
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  3. #3
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    Quote Originally Posted by skeeter View Post
    you have the correct approach ... \frac{x^2-1}{x} = x - \frac{1}{x}

    antiderivative is \frac{x^2}{2} - \ln|x| + C
    Thanks a lot,

    I forgot to mention that f(1) = 1/2, and f(-1) = 0
    When I solve for c, I get two different values when x=1 and x=-1.
    (C=0 when x=1, C=1/2 when x=-1)

    Does this mean C=0 when x>0 and C=1/2 when x<0?
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  4. #4
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    Quote Originally Posted by ty2391 View Post
    Thanks a lot,

    I forgot to mention that f(1) = 1/2, and f(-1) = 0
    When I solve for c, I get two different values when x=1 and x=-1.
    (C=0 when x=1, C=1/2 when x=-1)

    Does this mean C=0 when x>0 and C=1/2 when x<0?
    looks that way, doesn't it?
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