Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 4 - Integrals - 4.5 The Substitution Rule - 4.5 Exercises: 18

Answer

$cos(cos(x))+C$

Work Step by Step

Evaluate the Integral using substitution: $\int sinxsin(cosx)dx$ Substitution Rule: $\int f(g(x))gā€™(x)dx = \int f(u)du$ $u= cosx$ $du =-sinx$ Since $du$ in the expression is $sinx$ it must be multiplied by $-1$ Solve the integral in terms of $u$: $\int sin(u)(-1)du$ $-1\int sin(u)du $ $-1(-cos(u)) +C$ $cos(u) + C$ Substitute for $u$: $cos(cos(x)) +C$
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