Answer
$\frac{2}{5}(t+1)^{5/2}+c$
Work Step by Step
Let $u=t+1$, then $du=dt$. Now, we have
$$\int (t+1)\sqrt{t+1}dt= \int u \sqrt u du=\int u^{3/2}du\\
=\frac{1}{5/2}u^{5/2}+c=\frac{2}{5}(t+1)^{5/2}+c$$
Calculus (3rd Edition)
by Rogawski, Jon; Adams, Colin
Published by
W. H. Freeman
ISBN 10:
1464125260
ISBN 13:
978-1-46412-526-3
Chapter 7 - Exponential Functions - 7.8 Inverse Trigonometric Functions - Exercises - Page 375: 92
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