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: 13


$\frac{sec(3t)}{3} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int sec(3t)tan(3t)dt$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= 3t$ $du =3$ Since $du$ in the expression is equal to $1$ it must be multiplied by $\frac{1}{3} $ Solve the integral in terms of $u$: $\int sec(u)tan(u)(\frac{1}{3})du$ $\frac{1}{3}\int sec(u)tan(u)du $ $\frac{1}{3}sec(u) +C$ $\frac{sec(u)}{3} + C$ Substitute for $u$: $\frac{sec(3t)}{3} +C$
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