Carry out the integration as it stands, (you get two logs which can then be combined), and then ask yourself what value C must take in order that the integrand is not infinite at the top limit.
Find the value of the constant C for which the integral converges. Evaluate the integral for this value of C.
I dont understand how you can find a constant C for convergence, I thought that the only way to test for convergence, is by actually evaluating the integral or using the comparison test.