Answer
$$
\int(2x+7 )^{3/2} dx
=\frac{1}{5} (2x+7)^{5/2}+c.
$$
Work Step by Step
Since $ u=2x+7 $, then $ du=2dx $ and hence, $$
\int(2x+7 )^{3/2} dx=\frac{1}{2}\int u^{3/2} d u=\frac{1}{2} \frac{2}{5}u^{5/2}+c\\
=\frac{1}{5} (2x+7)^{5/2}+c.
$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 5 - The Integral - 5.7 Substitution Method - Exercises - Page 275: 10
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