Improper integral problem. $\int_9^\infty dx / [(x-8) (x-7)]$ I worked the problem out and ended up with $\ln(x-8) - \ln (x-7)$. So according to the natural log rule, I can make the problem $\ln (x-8)/(x-7)$. And then when I plug 9 in, I end up with 1/2 as the answer. But the real answer is 2. Did I do the rule wrong? Is it $\ln (x-7)/(x-8)$?
Also, if someone could please explain how to tell when an integral is converging/diverging, that would be really helpful. 

You did everything right. The indefinite integral is $$\ln{\frac{x-8}{x-7}}$$ At the two endpoints, you get $$\ln(1)-\ln({1\over 2})=\ln(2)$$
