Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 7

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

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