$$$u^{\frac{2}{3}}$$$의 적분

$$$\int u^{\frac{2}{3}}\, du$$$을(를) 구하시오.

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

$${\color{red}{\int{u^{\frac{2}{3}} d u}}}={\color{red}{\frac{u^{\frac{2}{3} + 1}}{\frac{2}{3} + 1}}}={\color{red}{\left(\frac{3 u^{\frac{5}{3}}}{5}\right)}}$$

따라서,

$$\int{u^{\frac{2}{3}} d u} = \frac{3 u^{\frac{5}{3}}}{5}$$

적분 상수를 추가하세요:

$$\int{u^{\frac{2}{3}} d u} = \frac{3 u^{\frac{5}{3}}}{5}+C$$

$$$\int u^{\frac{2}{3}}\, du = \frac{3 u^{\frac{5}{3}}}{5} + C$$$A