Chapter 8.7, Problem 3E

To determine

To prove: ${\displaystyle \underset{1}{\overset{\infty }{\int }}{x}^{-\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}dx$diverges by showing that the limit $\underset{R\to \infty }{\lim }{\displaystyle \underset{1}{\overset{R}{\int }}{x}^{-\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}dx=\infty$.