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: 31


$3 \ln |\sin(\frac{θ}{3})|+C$

Work Step by Step

$\int cot(\frac{θ}{3})dθ$ let $u=\frac{θ}{3}$ $du=\frac{1}{3}dθ$ $dθ=3$ $du$ $\int cot(\frac{θ}{3}dθ$ $=\int cot(u) (3)du$ $=3\int cot (u)du$ $=3 ln|sin(u)| +C$ $=3 ln |sin(\frac{θ}{3})|+C$
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