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 - 8.6 Exercises - Page 556: 67

Answer

$${\text{False}}$$

Work Step by Step

$$\eqalign{ & {\text{False, we can use a substitution to set the integrand to a integration}} \cr & {\text{formula}}{\text{.}} \cr & {\text{Example}} \cr & \int {\frac{{{e^x}}}{{1 - \tan {e^x}}}} dx \cr & {\text{Is we set }}u = {e^x},{\text{ }}du = {e^x}dx \cr & \int {\frac{{{e^x}}}{{1 - \tan {e^x}}}} dx = \int {\frac{{du}}{{1 - \tan u}}} \cr & {\text{Now we can apply formula 72}} \cr & \int {\frac{1}{{1 \pm \tan u}} = \frac{1}{2}\left( {u \pm \ln \left| {\cos u \pm \sin u} \right|} \right) + C} \cr} $$
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