Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 4 - Integration - 4.3 Integration By Substitution - Exercises Set 4.3 - Page 286: 37



Work Step by Step

Perform a u-substitution with $u=a+bx$. $du=b dx$, so $\frac{dx}{b}=dx$. This leaves $\frac{1}{b}\int{u^n}du$, which is $\frac{u^{n+1}}{b(n+1)}+C$. Converting back into terms of $x$ yields $=\frac{(a+bx)^{n+1}}{b(n+1)}+C$.
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