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

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

$ \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 $