integrate the problem below. choose the best answer. ∫(3√x)dx

Explanation:

Step1: Rewrite the square - root as a power

We know that $\sqrt{x}=x^{\frac{1}{2}}$, so the integral becomes $\int(3x^{\frac{1}{2}})dx$.

Step2: Use the power - rule for integration

The power - rule for integration is $\int x^{n}dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). Here $n=\frac{1}{2}$ and the coefficient is 3. So $\int(3x^{\frac{1}{2}})dx=3\int x^{\frac{1}{2}}dx$. $3\times\frac{x^{\frac{1}{2}+1}}{\frac{1}{2}+1}+C$.

Step3: Simplify the expression

First, $\frac{1}{2}+1=\frac{3}{2}$. Then $3\times\frac{x^{\frac{3}{2}}}{\frac{3}{2}}+C$. Since $3\times\frac{2}{3}x^{\frac{3}{2}}+C = 2x^{\frac{3}{2}}+C$.

Answer:

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