Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 13

$$ \frac{1}{8}$$

\begin{aligned} \int_{2}^{\infty} x^{-3} d x &=\lim _{R \rightarrow \infty} \int_{2}^{R} x^{-3} d x \\ &=\lim _{R \rightarrow \infty}\left.\frac{x^{-2}}{-2}\right|_{2} ^{R} \\ &=\lim _{R \rightarrow \infty}\frac{1}{8}-\frac{1}{2 R^{2}}\\ &= \frac{1}{8} \end{aligned}