$$$\frac{x^{31}}{9}$$$의 적분

$$$\int \frac{x^{31}}{9}\, dx$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=\frac{1}{9}$$$와 $$$f{\left(x \right)} = x^{31}$$$에 적용하세요:

$${\color{red}{\int{\frac{x^{31}}{9} d x}}} = {\color{red}{\left(\frac{\int{x^{31} d x}}{9}\right)}}$$

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=31$$$에 적용합니다:

$$\frac{{\color{red}{\int{x^{31} d x}}}}{9}=\frac{{\color{red}{\frac{x^{1 + 31}}{1 + 31}}}}{9}=\frac{{\color{red}{\left(\frac{x^{32}}{32}\right)}}}{9}$$

따라서,

$$\int{\frac{x^{31}}{9} d x} = \frac{x^{32}}{288}$$

적분 상수를 추가하세요:

$$\int{\frac{x^{31}}{9} d x} = \frac{x^{32}}{288}+C$$

$$$\int \frac{x^{31}}{9}\, dx = \frac{x^{32}}{288} + C$$$A