evaluate the following indefinite integral. ∫ 3/√x dx ∫ 3/√x dx = □

Answer:

$6\sqrt{x}+C$

Explanation:

Step1: Rewrite the integrand

Rewrite $\frac{3}{\sqrt{x}}$ as $3x^{-\frac{1}{2}}$. So the integral becomes $\int 3x^{-\frac{1}{2}}dx$.

Step2: Apply the power - rule for integration

The power - rule for integration is $\int x^n dx=\frac{x^{n + 1}}{n+1}+C$ ($n\neq - 1$). For $\int 3x^{-\frac{1}{2}}dx$, we have $n=-\frac{1}{2}$. Then $3\int x^{-\frac{1}{2}}dx=3\times\frac{x^{-\frac{1}{2}+1}}{-\frac{1}{2}+1}+C$.

Step3: Simplify the expression

$3\times\frac{x^{\frac{1}{2}}}{\frac{1}{2}}+C = 6\sqrt{x}+C$.