Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 415: 7

$\frac{{{x^2}}}{2} + \sin x + C$

$$\eqalign{ & \int {\left( {x + \cos x} \right)} dx \cr & {\text{Use the sum rule for integration}} \cr & = \int x dx + \int {\cos x} dx \cr & {\text{Apply: }}\int {{x^n}} dx = \frac{{{x^{n + 1}}}}{{n + 1}} + C{\text{ and }}\int {\cos xdx} = \sin x + C \cr & = \frac{{{x^{1 + 1}}}}{{1 + 1}} + \sin x + C \cr & {\text{Simplify}} \cr & = \frac{{{x^2}}}{2} + \sin x + C \cr} $$