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March 27, 2017

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can someone help me find the antiderivative of:

f'(x) = (x^2-1)/x where f(1)=1/2, and f(-1) = 0

Thanks!

  • calculus - antiderivative - ,

    f'(x) = x - 1/x
    Integrate one term at a time.
    f(x) = x^2/2 - ln x + C

    If f(1) = 1/2, then C = 0
    (for x>0 only)

    I'm not sure how to handle the f(-1) = 0 case. You can't take a log of a negative number.

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