Thread: anti-derivative of something raised to the -1?

1. anti-derivative of something raised to the -1?

In my case, what would be the antiderivative of (9-6x)^-1

2. Is this a definite integral?

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

In another form:
$\displaystyle \int_1^x t^{-1}dt=lnx$ for $\displaystyle x>0$

You can then use U-Substitution to manipulate your problem to fit these parameters.

3. 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.