$$$t^{\frac{5}{2}}$$$의 적분

$$$\int t^{\frac{5}{2}}\, dt$$$을(를) 구하시오.

멱법칙($$$\int t^{n}\, dt = \frac{t^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=\frac{5}{2}$$$에 적용합니다:

$${\color{red}{\int{t^{\frac{5}{2}} d t}}}={\color{red}{\frac{t^{1 + \frac{5}{2}}}{1 + \frac{5}{2}}}}={\color{red}{\left(\frac{2 t^{\frac{7}{2}}}{7}\right)}}$$

따라서,

$$\int{t^{\frac{5}{2}} d t} = \frac{2 t^{\frac{7}{2}}}{7}$$

적분 상수를 추가하세요:

$$\int{t^{\frac{5}{2}} d t} = \frac{2 t^{\frac{7}{2}}}{7}+C$$

$$$\int t^{\frac{5}{2}}\, dt = \frac{2 t^{\frac{7}{2}}}{7} + C$$$A