Calculus: Early Transcendentals (2nd Edition)

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

Chapter 7 - Integration Techniques - 7.1 Basic Approaches - 7.1 Exercises: 38

Answer

\[ = \int_{}^{} {x + \frac{2}{3}{x^{\frac{3}{2}}} + C} \]

Work Step by Step

\[\begin{gathered} \int_{}^{} {\frac{{1 - x}}{{1 - \sqrt x }}} \,dx \hfill \\ \hfill \\ {\text{rationalizing}} \hfill \\ \hfill \\ \int_{}^{} {\frac{{\,\left( {1 - \sqrt x } \right)\,\left( {1 + \sqrt x } \right)}}{{1 - \sqrt x }}} \,dx \hfill \\ \hfill \\ = \int_{}^{} {\,\left( {1 + \sqrt x } \right)} \,\,dx \hfill \\ \hfill \\ or \hfill \\ \hfill \\ \int {dx} + \int {{x^{1/2}}} dx \hfill \\ \hfill \\ integrate \hfill \\ \hfill \\ = \int_{}^{} {x + \frac{2}{3}{x^{\frac{3}{2}}} + C} \hfill \\ \end{gathered} \]
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