Calculus (3rd Edition)

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

Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 37


$$\frac{1}{36} (3x+8) ^{12}+c$$

Work Step by Step

Given $$\int (3x+8)^{11}d x$$ Let $$u=3x+8 \ \ \ \Rightarrow \ \ du=3dx $$ then \begin{align*} \int (3x+8)^{11}d x&=\frac{1}{3} \int u^{11}du \\ &=\frac{1}{36} u^{12}+c\\ &=\frac{1}{36} (3x+8) ^{12}+c \end{align*}
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