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: 14

Answer

\[ = \sin \,\left( {4{x^2} + 3} \right) + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {8x\cos \,\left( {4{x^2} + 3} \right)\,dx} \hfill \\ \hfill \\ set\,\,\,u = 4{x^2} + 3\,\,\,\,\,then\,\,\,\,du = 8xdx \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \int_{}^{} {\cos \,\left( u \right)du} \hfill \\ \hfill \\ {\text{integrating}} \hfill \\ \hfill \\ = \sin \,\left( u \right) + C \hfill \\ \hfill \\ substitute\,\,back\,\,u = 4{x^2} + 3 \hfill \\ \hfill \\ = \sin \,\left( {4{x^2} + 3} \right) + C \hfill \\ \end{gathered} \]
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