Calculus: Early Transcendentals (2nd Edition)

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

Chapter 5 - Integration - 5.5 Substitution Rule - 5.5 Exercises: 65

Answer

\[ = \frac{1}{{2{{\cot }^2}x}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{{{\csc }^2}x}}{{{{\cot }^3}x}}} \,\,dx \hfill \\ \hfill \\ u = \cot x\,\,\,\,then\,\,\,\,du = - {\csc ^2}xdx \hfill \\ \hfill \\ apply\,\,the\,\,\,substitution \hfill \\ \hfill \\ = \int_{}^{} { - \frac{{du}}{{{u^3}}}} \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \frac{1}{{2{u^2}}} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,\,u = \cot x \hfill \\ \hfill \\ = \frac{1}{{2{{\cot }^2}x}} + C \hfill \\ \hfill \\ \end{gathered} \]
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