Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 6 - Exponential, Logarithmic, And Inverse Trigonometric Functions - 6.3 Derivatives Of Inverse Functions; Derivatives And Integrals Involving Exponential Functions - Exercises Set 6.3: 67

Answer

$e^{\sin(x)}+C$

Work Step by Step

Using a u-substitution of $u=sin(x)$ yields $du=cos(x)dx$ and makes the integral $$\int{e^{u}}du=e^{u}+C$$ Replacing $u$ in terms of $x$ yields $\boxed{e^{\sin(x)}+C}$.
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