Chapter 8, Problem 18PS

To determine

To calculate: The approximate value of the integral ${\displaystyle {\int }_2^{\infty }\frac{1}{x^5-1}dx}$ using the inequality $\frac{1}{x^5}+\frac{1}{x^{10}}+\frac{1}{x^{15}}<\frac{1}{x^5-1}<\frac{1}{x^5}+\frac{1}{x^{10}}+\frac{2}{x^{15}}$