How do you evaluate the integral #int 1/(x-1) dx# from 0 to 2 if it converges?

1 Answer
Dec 22, 2016

The integral does not converge.

Explanation:

The integrand is not continuous on the interval #[0,2]#. We try to find the improper integral by evaluating

#lim_(brarr1^-)int_0^b 1/(x-1) dx# and #lim_(ararr1^+)int_a^2 1/(x-1) dx#.

If these two improper integral converge, then #int_0^2 1/(x-1) dx# is equal to the sum of the two numbers.

Since #int 1/(x-1) dx = ln abs(x-1) +C#, neither integral converges.