Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 7 - Exponential Functions - 7.1 Derivative of f(x)=bx and the Number e - Exercises - Page 328: 85


$2e^{\sqrt x}+c $

Work Step by Step

Recall that $(e^x)'=e^x$ Let $ u= \sqrt x $, then $ du=\frac{1}{2\sqrt x} dx $ and hence we have $$ \int \frac{e^{\sqrt x}}{\sqrt x} dx=2\int e^{u} du\\ =2e^u+c=2e^{\sqrt x}+c . $$
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