$$$x^{\frac{3}{2}}$$$의 적분

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

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

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

따라서,

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

적분 상수를 추가하세요:

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

$$$\int x^{\frac{3}{2}}\, dx = \frac{2 x^{\frac{5}{2}}}{5} + C$$$A