Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises: 7

Answer

$\int \frac{du}{u}$ $u=1-2\sqrt x$

Work Step by Step

Try it: $u=1-2x^\frac{1}{2}$ $du=-\frac{1}{2}2x^{-\frac{1}{2}}dx$ $du=-(x^{-\frac{1}{2}})dx$ $du=-\frac{1}{\sqrt x}dx$ $-\int \frac{1}{1-2\sqrt x}(\frac{-1}{\sqrt x})dx$ $- \int \frac{du}{u}$ $-ln|u|+C$ $-ln|1-2\sqrt x|+C$ $\int \frac{du}{u}$ $u=1-2\sqrt x$
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