Chapter 5 - Section 5.4 - Indefinite Integrals and the Net Change Theorem - 5.4 Exercises - Page 409: 13

$$\int(\sin x+\sinh x)dx=-\cos x+\cosh x+C$$

$$A=\int(\sin x+\sinh x)dx$$ From Table 1, $$\int[f(x)+g(x)]dx=\int f(x)dx+\int g(x)dx$$ Therefore, $$A=\int(\sin x)dx+\int(\sinh x)dx$$ From Table 1, we also get that $$\int (\sin x)dx=-\cos x+C$$ $$\int(\sinh x)dx=\cosh x+C$$ Therefore, $$A=-\cos x+\cosh x+C$$