Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 7 - Techniques of Integration - Review - Exercises - Page 578: 38


$$ 2 \left( \frac{2^{ \sqrt{x} }}{\ln 2}\right) +c$$

Work Step by Step

Given $$\int \frac{2^{\sqrt{x}}}{\sqrt{x}} d x$$ Let $u=\sqrt{x} \ \ \Rightarrow \ \ du =\dfrac{dx}{2\sqrt{x}} $, then \begin{align*} \int \frac{2^{\sqrt{x}}}{\sqrt{x}} d x&=2\int 2^{u } d u\\ &= 2 \left( \frac{2^{u }}{\ln 2}\right) +c\\ &= 2 \left( \frac{2^{ \sqrt{x} }}{\ln 2}\right) +c \end{align*}
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