Answer
$\int\frac{x+1}{x+2}dx=x-\ln|x+2|+C$
Work Step by Step
Substitution:
$u=x+2$
$x+1=u-1$
$dx=du$
$\int\frac{x+1}{x+2}dx=\int\frac{u-1}{u}du=\int(1-u^{-1})du=\int du-\int\frac{1}{u}du=u-\ln|u|+C=x+2-\ln|x+2|+C=x-\ln|x+2|+C$
Finite Math and Applied Calculus (6th Edition)
by Waner, Stefan; Costenoble, Steven
Published by
Brooks Cole
ISBN 10:
1133607705
ISBN 13:
978-1-13360-770-0
Chapter 13 - Review - Review Exercises - Page 1004: 17
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