Chapter 9.4, Problem 33E

To determine

Tostate: whether the integral converges or diverges using the comparison test.

Answer to Problem 33E

The integral is diverges.

Explanation of Solution

Given information:

The integral is ${\displaystyle {\int }_{\pi }^{\infty }\frac{2+\cos x}{x}dx}$ .

using the comparison test, the function of integral can be defined as:

  $0\le \frac{1}{x}\le \frac{2+\cos x}{x}$

On the interval $\text{[}\pi \text{,}\infty \text{)}$ and the integral ${\displaystyle {\int }_{\pi }^{\infty }\frac{1}{x}}$ diverges,

Thus, the integral is diverges.