Calculus 10th Edition

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

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 41

Answer

$\frac 1 2 ln|cos(\frac 2 t)|+C$

Work Step by Step

$Let u=cos(\frac 2 t), du=\frac {2sin(\frac 2 t)}{t^2}dt$ $\int \frac{tan\frac2 t}{t^2}dt$ $\frac1 2 \int \frac 1{cos(\frac 2 t)}[\frac {2sin(\frac 2 t)}{t^2}]dt$ $\frac 1 2 ln|cos(\frac 2 t)|+C$
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