Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.6 Other Integration Strategies - 7.6 Exercises: 7

Answer

\[ = \ln \left| {x + \sqrt {{x^2} + 16} } \right| + C\]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + 16} }}} \hfill \\ \hfill \\ use\,\,the\,\,formula\,\,\int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + {a^2}} }}} \hfill \\ with\,a = 4 \hfill \\ \hfill \\ then \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ \int_{}^{} {\frac{{dx}}{{\sqrt {{x^2} + 16} }}} = \ln \left| {x + \sqrt {{x^2} + {a^2}} } \right| + C \hfill \\ \hfill \\ therefore \hfill \\ \hfill \\ = \ln \left| {x + \sqrt {{x^2} + 16} } \right| + C \hfill \\ \hfill \\ \end{gathered} \]
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