To determine the convergence or divergence of the integral, how many improper integrals must be analyzed? What must be true of each of these integrals if the given integral converges?
I think it must be analyzed twice. Even if that is right, I don't know what must be true of each of them if they converge.
(I chose to split the first interval at 1, but you could use any value between 0 and 2)
If any of these three limits does not exist, then the original integral does not converge. For the antiderivative, use partial fraction decomposition.