$$$g_{3}$$$에 대한 $$$g_{3} r^{5}$$$의 적분

$$$\int g_{3} r^{5}\, dg_{3}$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(g_{3} \right)}\, dg_{3} = c \int f{\left(g_{3} \right)}\, dg_{3}$$$을 $$$c=r^{5}$$$와 $$$f{\left(g_{3} \right)} = g_{3}$$$에 적용하세요:

$${\color{red}{\int{g_{3} r^{5} d g_{3}}}} = {\color{red}{r^{5} \int{g_{3} d g_{3}}}}$$

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

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

따라서,

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

적분 상수를 추가하세요:

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

$$$\int g_{3} r^{5}\, dg_{3} = \frac{g_{3}^{2} r^{5}}{2} + C$$$A