Answer
$(x+1)^3+c$
Work Step by Step
Separate the differentials and integrate.
$\int 3(x+1)^2dx=\int (\dfrac{y-1}{y})dy$
or, $3\int (x+1)^2dx=\int (1-\dfrac{1}{y})dy$
This implies that $y-\ln y=\dfrac{3(x+1)^3}{3}+c$
Thus, $y-\ln y=(x+1)^3+c$
University Calculus: Early Transcendentals (3rd Edition)
by Hass, Joel R.; Weir, Maurice D.; Thomas Jr., George B.
Published by
Pearson
ISBN 10:
0321999584
ISBN 13:
978-0-32199-958-0
Chapter 7 - Practice Exercises - Page 421: 28
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