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