$$$\frac{1}{x^{\frac{8}{3}}}$$$의 적분

$$$\int \frac{1}{x^{\frac{8}{3}}}\, dx$$$을(를) 구하시오.

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=- \frac{8}{3}$$$에 적용합니다:

$${\color{red}{\int{\frac{1}{x^{\frac{8}{3}}} d x}}}={\color{red}{\int{x^{- \frac{8}{3}} d x}}}={\color{red}{\frac{x^{- \frac{8}{3} + 1}}{- \frac{8}{3} + 1}}}={\color{red}{\left(- \frac{3 x^{- \frac{5}{3}}}{5}\right)}}={\color{red}{\left(- \frac{3}{5 x^{\frac{5}{3}}}\right)}}$$

따라서,

$$\int{\frac{1}{x^{\frac{8}{3}}} d x} = - \frac{3}{5 x^{\frac{5}{3}}}$$

적분 상수를 추가하세요:

$$\int{\frac{1}{x^{\frac{8}{3}}} d x} = - \frac{3}{5 x^{\frac{5}{3}}}+C$$

$$$\int \frac{1}{x^{\frac{8}{3}}}\, dx = - \frac{3}{5 x^{\frac{5}{3}}} + C$$$A