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 275: 23


$$\frac{1}{4}\sin (x^4) +c $$

Work Step by Step

Given $$\int x^{3} \cos \left(x^{4}\right) d x$$ Let $$ u= x^4\ \ \ \Rightarrow \ \ \ du=4x^3dx$$ Then \begin{align*} \int x^{3} \cos \left(x^{4}\right) d x&= \int \frac{1}{4} \cos \left(u\right) du\\ &= \frac{1}{4}\sin u +c\\ &=\frac{1}{4}\sin (x^4) +c \end{align*}
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