Answer
$$A=5x+\frac{2x^3}{9}+\frac{3x^4}{16}+C$$
Work Step by Step
$$A=\int(5+\frac{2}{3}x^2+\frac{3}{4}x^3)dx$$ From Table 1, $$\int cf(x)dx=c\int f(x)dx$$ $$\int[f(x)+g(x)]dx=\int f(x)dx+\int g(x)dx$$ Therefore, $$A=\int5dx+\frac{2}{3}\int(x^2)dx+\frac{3}{4}\int(x^3)dx$$
From Table 1, we also get the followings $$\int kdx=kx+C$$ $$\int (x^n)dx=\frac{x^{n+1}}{n+1}$$
Therefore, $$A=5x+\frac{2}{3}\frac{x^3}{3}+\frac{3}{4}\frac{x^4}{4}+C$$
$$A=5x+\frac{2x^3}{9}+\frac{3x^4}{16}+C$$
