Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.3 Exercises: 25

Answer

$\frac{\sec^52t}{10} - \frac{\sec^32t}{6} +C$

Work Step by Step

Find the indefinite integral $\int tan^32t sec^32tdt$ $\int tan^2(2t)sec^2(2t) sec(2t)tan(2t)dt$, Break the integral up $\int (sec^22t-1) sec^2(2t) sec(2t) tan(2t) dt$ $\int(sec^42t -sec^22t) sec(2t) tan(2t)dt$ Let $u=sec2t$, and $du=2sec(2t)tan(2t)dt$ $\frac{1}{2}\int u^4du - \frac{1}{2}\int u^2du$, U-substitution $\frac{u^5}{10} - \frac{u^3}{6}+C$ $\frac{\sec^52t}{10} - \frac{\sec^32t}{6} +C$
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