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: 46


$F(x)$ is the antiderivative of $f(x)$.

Work Step by Step

We have $$ (\frac{1}{a(n+1)}(a x+b)^{n+1}+C)'=\frac{n+1}{a(n+1)}(a x+b)^{n}(a)=(a x+b)^{n}$$ that is, $\int(a x+b)^{n} d x=\frac{1}{a(n+1)}(a x+b)^{n+1}+C$.
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