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Math Help - anti-derivative of something raised to the -1?

  1. #1
    Junior Member BugzLooney's Avatar
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    anti-derivative of something raised to the -1?

    In my case, what would be the antiderivative of (9-6x)^-1
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  2. #2
    Newbie Riyzar's Avatar
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    Is this a definite integral?

    If so note that:
    \int_1^x \frac{1}{t}dt=lnx for x>0


    In another form:
    \int_1^x t^{-1}dt=lnx for x>0<br />

    You can then use U-Substitution to manipulate your problem to fit these parameters.
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  3. #3
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    for a function in the form of (ax+b)^-1, the antiderivative is (ln(ax+b)/a) +c,
    so in your case:

    the antiderivative would be (ln(-6x+9) / -6)+c.
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