(2) $\\int 5x^{7}dx =$

Explanation:

Step1: Use the property of integral $\int kf(x)dx=k\int f(x)dx$

$$\int5x^{7}dx = 5\int x^{7}dx$$

Step2: Apply the power - rule for integration $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C(n\neq - 1)$

For $n = 7$, we have $5\times\frac{x^{7+1}}{7 + 1}+C$ $$5\times\frac{x^{8}}{8}+C=\frac{5}{8}x^{8}+C$$

Answer:

$\frac{5}{8}x^{8}+C$