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: 21

Answer

\[ = \frac{{\,{{\left( {{x^2} + x} \right)}^{11}}}}{{11}} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\,{{\left( {{x^2} + x} \right)}^{10}}\,\left( {2x + 1} \right)dx} \hfill \\ \hfill \\ set\,\,the\,\,substitution \hfill \\ \hfill \\ u = {x^2} + x\,\,\,\,\,\,\,then\,\,\,\,\,du = \,\left( {2x + 1} \right)dx \hfill \\ \hfill \\ thererore \hfill \\ \hfill \\ \int_{}^{} {{u^{10}}du} \hfill \\ \hfill \\ integrate\,\, \hfill \\ \hfill \\ = \frac{{{u^{11}}}}{{11}} + C \hfill \\ \hfill \\ replace\,\,u\,\,with\,\,u = {x^2} + x \hfill \\ \hfill \\ = \frac{{\,{{\left( {{x^2} + x} \right)}^{11}}}}{{11}} + C \hfill \\ \hfill \\ \end{gathered} \]
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