Answer
$\frac{1}{5}\tan 5x+C$
Work Step by Step
Use the substitution $u=5x$. Then $du=5dx$, so $dx=\frac{1}{5} du$.
$\int\sec^2 5x dx$
$=\int \sec^2 u*\frac{1}{5}du$
$=\int \frac{1}{5}\sec^2 udu$
$=\frac{1}{5}\tan u+C$
$=\frac{1}{5}\tan 5x+C$
Calculus, 10th Edition (Anton)
by Anton, Howard
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: 16
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