Find the value of the constant C for which the integral $\displaystyle \int_{0}^{\infty}(\frac{1}{\sqrt{x^{2} + 4}} -\frac{C}{x + 2})dx$ 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.