Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 7 - Integration Techniques - 7.3 Trigonometric Integrals - 7.3 Exercises: 25

Answer

\[ = \tan x - x + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{{\tan }^2}xdx} \hfill \\ \hfill \\ write\,\,\,{\tan ^2}x = {\sec ^2}x - 1 \hfill \\ \hfill \\ = \int_{}^{} {\,\left( {{{\sec }^2}x - 1} \right)} \,\,dx \hfill \\ \hfill \\ {\text{split}}\,\,{\text{the}}\,\,{\text{integrand}} \hfill \\ \hfill \\ = \int_{}^{} {{{\sec }^2}xdx\, - \int_{}^{} {dx} } \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \tan x - x + C \hfill \\ \end{gathered} \]
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