Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 8 - Techniques of Integration - 8.7 Improper Integrals - Exercises - Page 440: 14



Work Step by Step

\begin{aligned} \int_{0}^{\infty} \frac{d x}{(x+1)^{3}} &=\lim _{R \rightarrow \infty} \int_{0}^{R} \frac{d x}{(x+1)^{3}} \\ &=\lim _{R \rightarrow \infty} \left.\frac{(x+1)^{-2}}{-2}\right|_{0} ^{R} \\ &=\lim _{R \rightarrow \infty} \frac{1}{2}-\frac{1}{2} \frac{1}{(R+1)^{2}} \\ &=\frac{1}{2} \end{aligned}
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