Answer
$5\ln \left( e^x+2\right) +c$
Work Step by Step
$v=e^{x}+2\Rightarrow dv=e^{x}dx$
$$\Rightarrow \int \dfrac {5e^x}{e^x+2}dx=\int 5\dfrac {dv}{v}=5\ln v+c=5\ln \left( e^x+2\right) +c$$
Calculus Concepts: An Informal Approach to the Mathematics of Change 5th Edition
by LaTorre, Donald R.; Kenelly, John W.; Reed, Iris B.; Carpenter, Laurel R.; Harris, Cynthia R.
Published by
Brooks Cole
ISBN 10:
1-43904-957-2
ISBN 13:
978-1-43904-957-0
Chapter 5 - Accumulating Change: Limits of Sums and the Definite Integral - 5.9 Activities - Page 409: 8
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