Calculus (3rd Edition)

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

Chapter 5 - The Integral - 5.3 The Indefinite Integral - Exercises - Page 252: 23


$\int(t^{\frac{1}{2}}+1) (t+1) dt= \frac{2}{5}t^{\frac{5}{2}}+ \frac{2}{3}t^{\frac{3}{2}}+ \frac{1}{2}t^2 +C $

Work Step by Step

$\int(t^{\frac{1}{2}}+1) (t+1) dt= \int(t^{\frac{3}{2}}+t^{\frac{1}{2}}+t+1) dt= \frac{1}{\frac{5}{2}}t^\frac{5}{2} + \frac{1}{\frac{3}{2}} t^{\frac{3}{2}}+\frac{1}{2}t^2 +t +C= \frac{2}{5}t^{\frac{5}{2}}+ \frac{2}{3}t^{\frac{3}{2}}+ \frac{1}{2}t^2 +C $
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