$$$x^{3} \sqrt{x^{21}}$$$의 적분

$$$\int x^{3} \sqrt{x^{21}}\, dx$$$을(를) 구하시오.

입력이 다음과 같이 다시 쓰입니다: $$$\int{x^{3} \sqrt{x^{21}} d x}=\int{x^{\frac{27}{2}} d x}$$$.

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=\frac{27}{2}$$$에 적용합니다:

$${\color{red}{\int{x^{\frac{27}{2}} d x}}}={\color{red}{\frac{x^{1 + \frac{27}{2}}}{1 + \frac{27}{2}}}}={\color{red}{\left(\frac{2 x^{\frac{29}{2}}}{29}\right)}}$$

따라서,

$$\int{x^{\frac{27}{2}} d x} = \frac{2 x^{\frac{29}{2}}}{29}$$

적분 상수를 추가하세요:

$$\int{x^{\frac{27}{2}} d x} = \frac{2 x^{\frac{29}{2}}}{29}+C$$

$$$\int x^{3} \sqrt{x^{21}}\, dx = \frac{2 x^{\frac{29}{2}}}{29} + C$$$A