Calculus with Applications (10th Edition)

Published by Pearson
ISBN 10: 0321749006
ISBN 13: 978-0-32174-900-0

Chapter 7 - Integration - 7.1 Antiderivatives - 7.1 Exercises: 16

Answer

\[\frac{{{x^7}}}{7} + {x^4} + {x^3} + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {{x^2}\,\left( {{x^4} + 4x + 3} \right)dx} \hfill \\ Multiplying \hfill \\ \int_{}^{} {\,\left( {{x^6} + 4{x^3} + 3{x^2}} \right)dx} \hfill \\ using\,\,the\,\,sum\,\,and\,difference\,\,rules \hfill \\ \int_{}^{} {{x^6}dx} + \int_{}^{} {4{x^3}dx} + \int_{}^{} {3{x^2}dx} \hfill \\ Use\,\,the\,\,power\,\,rule \hfill \\ \int_{}^{} {{x^n}dx} = \frac{{{x^{n + 1}}}}{{n + 1}} + C \hfill \\ \frac{{{x^{6 + 1}}}}{{6 + 1}} + 4\,\left( {\frac{{{x^{3 + 1}}}}{{3 + 1}}} \right) + 3\,\left( {\frac{{{x^2} + 1}}{{2 + 1}}} \right) + C \hfill \\ \frac{{{x^7}}}{7} + {x^4} + {x^3} + C \hfill \\ \end{gathered} \]
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