I have no idea where to start with improper integrals... I'm trying to solve the integral of 1/(x^2)-25 dx from 6 to infinity and I have no clue how to begin. Also, how do I recognize if it is divergent?
First note that
.
Now note that .
Now when you evalute , its the same as .
Spoiler:
Does this make sense?
To answer the last question. If the integral is similar to , and , then the integral is divergent. Also, the integral can be divergent if the integrand crosses a vertical asymptote.
EDIT: Plato and Kriz beat me...