Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 15

$$2$$

\begin{aligned} \int_{-3}^{\infty} \frac{d x}{(x+4)^{3 / 2}} &=\lim _{R \rightarrow \infty} \int_{-3}^{R} \frac{d x}{(x+4)^{3 / 2}} \\ &=\lim _{R \rightarrow \infty} \left.\frac{(x+4)^{(-1 / 2)}}{-1 / 2}\right|_{-3} ^{R} \\ &=\lim _{R \rightarrow \infty} \left(2-\frac{2}{(R+4)(1 / 2)} \right)\\ &= 2\end{aligned}