Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 8 - Integration Techniques, L'Hopital's Rule, and Improper Integrals - 8.1 Exercises - Page 512: 4

Answer

(c) $ \frac{1}{2} \sin{ (x^2+1) } + C$

Work Step by Step

$ \frac{dy}{dx} = x \cos{ (x^2 +1) } $ $ \int{ x \cos{ (x^2+1) } dx } $ $ \int{ x \cos{(u)} \frac{du}{2x} } $ Substitution: $ u=x^2+1 $ $ \frac{1}{2} \int{ \cos{(u)} du } $ $ \frac{1}{2} (\sin{u} + C) $ $ \frac{1}{2} \sin{ (x^2+1) } + C $
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