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: 46

Answer

\[ = \ln \left| {\sin x} \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\cot \,xdx} \hfill \\ \hfill \\ use\,\,\,\,\cot x = \frac{{\cos x}}{{\sin x}} \hfill \\ \hfill \\ \int_{}^{} {\cot xdx\, = \int_{}^{} {\frac{{\cos x}}{{\sin x}}dx} } \hfill \\ \hfill \\ set\,\,u = \sin x\,\,then\,\,du = \cos xdx \hfill \\ \hfill \\ \int_{}^{} {\frac{{\cos x}}{{\sin x}}\,dx} = \int_{}^{} {\frac{{du}}{u}} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \ln \left| u \right| + C \hfill \\ \hfill \\ \,\,u\, = \,\sin \,x\,\,then \hfill \\ \hfill \\ = \ln \left| {\sin x} \right| + C \hfill \\ \end{gathered} \]
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