$$$\frac{1}{x^{\frac{2}{3}}}$$$의 적분

$$$\int \frac{1}{x^{\frac{2}{3}}}\, dx$$$을(를) 구하시오.

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=- \frac{2}{3}$$$에 적용합니다:

$${\color{red}{\int{\frac{1}{x^{\frac{2}{3}}} d x}}}={\color{red}{\int{x^{- \frac{2}{3}} d x}}}={\color{red}{\frac{x^{- \frac{2}{3} + 1}}{- \frac{2}{3} + 1}}}={\color{red}{\left(3 x^{\frac{1}{3}}\right)}}={\color{red}{\left(3 \sqrt[3]{x}\right)}}$$

따라서,

$$\int{\frac{1}{x^{\frac{2}{3}}} d x} = 3 \sqrt[3]{x}$$

적분 상수를 추가하세요:

$$\int{\frac{1}{x^{\frac{2}{3}}} d x} = 3 \sqrt[3]{x}+C$$

$$$\int \frac{1}{x^{\frac{2}{3}}}\, dx = 3 \sqrt[3]{x} + C$$$A