# Math Help - Evaluating improper integral for constant (C)

1. ## Evaluating improper integral for constant (C)

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

2. 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.