Calculus 10th Edition

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

Chapter 5 - Logarithmic, Exponential, and Other Transcendental Functions - 5.2 Exercises - Page 334: 36



Work Step by Step

$\int(2- tan(\frac{θ}{4}) )dθ$ $=\int 2dθ$ $-\int tan(\frac{θ}{4}) dθ$ for $\int tan(\frac{θ}{4}) dθ$, let $u=\frac{θ}{4}$ $du=\frac{1}{4} dθ$ $dθ=4du$ $\int tan(\frac{θ}{4}) dθ$ $=4\int tan(u)$ $du$ $=4(-ln|cos(u)|$ $=-4ln|cos(\frac{θ}{4})|$ $\int 2dθ$ $-\int tan(\frac{θ}{4}) dθ$ $=2θ-(-4ln|cos(\frac{θ}{4})|)+C$ $=2θ+4ln|cos(\frac{θ}{4})|+C$
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