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: 24

Answer

$2\sqrt{1+tant} +C$

Work Step by Step

Evaluate the Integral using substitution: $\int \frac{dt}{cos^2t\sqrt{1+tant}}$ Substitution Rule: $\int f(g(x))g’(x)dx = \int f(u)du$ $u= 1+tant$ $du =sec^2t = \frac{1}{cos^2t}$ Solve the integral in terms of $u$: $\int \frac{1}{\sqrt u}du$ $2\sqrt u +C$ Substitute for $u$: $2\sqrt{1+tant} +C$
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