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: 12

Answer

$$ \int (x^3+1)\cos (x^4+4x ) dx =\frac{1}{4} \sin (x^4+4x ) +c. $$

Work Step by Step

Since $ u=x^4+4x $, then $ du=4(x^3+1)dx $ and hence, $$ \int (x^3+1)\cos (x^4+4x ) dx=\frac{1}{4}\int \cos u d u=\frac{1}{4} \sin u+c\\ =\frac{1}{4} \sin (x^4+4x ) +c. $$
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