Answer
$$A=\frac{u^7}{7}-\frac{u^6}{3}-\frac{u^4}{4}+\frac{2u}{7}+C$$
Work Step by Step
$$A=\int(u^6-2u^5-u^3+\frac{2}{7})du$$ 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, $$A=\int(u^6)du-2\int(u^5)du-\int(u^3)du+\int\frac{2}{7}du$$
From Table 1, we also get the followings $$\int kdx=kx+C$$ $$\int (x^n)dx=\frac{x^{n+1}}{n+1}$$
Therefore, $$A=\frac{u^7}{7}-2\frac{u^6}{6}-\frac{u^4}{4}+\frac{2u}{7}+C$$ $$A=\frac{u^7}{7}-\frac{u^6}{3}-\frac{u^4}{4}+\frac{2u}{7}+C$$
