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: 16

Answer

$\frac{1}{5}\tan 5x+C$

Work Step by Step

Use the substitution $u=5x$. Then $du=5dx$, so $dx=\frac{1}{5} du$. $\int\sec^2 5x dx$ $=\int \sec^2 u*\frac{1}{5}du$ $=\int \frac{1}{5}\sec^2 udu$ $=\frac{1}{5}\tan u+C$ $=\frac{1}{5}\tan 5x+C$
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