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Match the following improper integral with the improper integral below in which you can compare using the Comparison Test. Then determine whether the integral converge or diverge.

A. $\displaystyle \int_1^{\infty}\! \frac{dx}{x}$ , B. $\displaystyle \int_1^{\infty}\! \frac{dx}{x^2}$ , C. $\displaystyle \int_1^{\infty}\! \frac{dx}{x^3}$ , and D. $\displaystyle \int_1^{\infty}\! \frac{dx}{\sqrt{x}}$

1. $\displaystyle \int_1^{\infty}\! \frac{dx}{x^{2}+5}$ Does this integral converge or diverge?

2. $\displaystyle \int_1^{\infty}\! \frac{2+e^{-x}}{\sqrt{x}}\, dx$ Does this integral converge or diverge?

3. $\displaystyle \int_1^{\infty}\! \frac{x}{x^{2}-0.5}\, dx$ Does this integral converge or diverge?

4. $\displaystyle \int_1^{\infty}\! \frac{2+\cos x}{x}\, dx$ Does this integral converge or diverge?

In order to get credit for this problem all answers must be correct.