Calculus (3rd Edition)

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 276: 86



Work Step by Step

Given $$\int f(x)^{3} f^{\prime}(x) \mathrm{d} x$$ Let $$ u=f(x) \ \ \ \Rightarrow \ \ \ du = f'(x) dx$$ Then \begin{aligned} \int f(x)^{3} f^{\prime}(x) \mathrm{d} x &=\int u^{3} \mathrm{d} u \\ &=\frac{u^{4}}{4}+C \\ &=\frac{(f(x))^{4}}{4}+C \end{aligned}
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