Answer
$${\text{ The integral converges}}$$
Work Step by Step
$$\eqalign{
& \int_1^\infty {\frac{1}{{{x^5}}}} dx \cr
& {\text{From the result of exercise 49 we obtain that}} \cr
& \int_1^\infty {\frac{1}{{{x^p}}}} dx{\text{ converges to }}\frac{1}{{p - 1}}{\text{ if }}p > 1 \cr
& \int_1^\infty {\frac{1}{{{x^5}}}} dx \Rightarrow p = 5,{\text{ }}p > 1,{\text{ }} \cr
& {\text{Then the integral converges to }}\frac{1}{{p - 1}} \cr
& \int_1^\infty {\frac{1}{{{x^5}}}} dx = \frac{1}{{5 - 1}} = \frac{1}{4} \cr} $$
