Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises - Page 346: 27


$\frac{sec^3(x)}{3} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int sec^3(x)tan(x)dx$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= sec(x)$ $du =sec(x)tan(x)$ Solve the integral in terms of $u$: $\int u^2du$ $\frac{u^3}{3}+C$ Substitute for $u$: $\frac{sec^3(x)}{3} +C$
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