(6) $\\int 20\\sqrt{x}dx$

Explanation:

Step1: Use integral constant multiple rule

$$\int 20\sqrt{x}dx=20\int x^{\frac{1}{2}}dx$$

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

For $n=\frac{1}{2}$, we have $20\times\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C$. Simplify the coefficient: $\frac{1}{\frac{1}{2}+1}=\frac{1}{\frac{3}{2}}=\frac{2}{3}$, so $20\times\frac{2}{3}x^{\frac{3}{2}}+C=\frac{40}{3}x^{\frac{3}{2}}+C$.

Answer:

$\frac{40}{3}x^{\frac{3}{2}}+C$