$$$x^{17} + x^{7}$$$의 적분

$$$\int \left(x^{17} + x^{7}\right)\, dx$$$을(를) 구하시오.

각 항별로 적분하십시오:

$${\color{red}{\int{\left(x^{17} + x^{7}\right)d x}}} = {\color{red}{\left(\int{x^{7} d x} + \int{x^{17} d x}\right)}}$$

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=7$$$에 적용합니다:

$$\int{x^{17} d x} + {\color{red}{\int{x^{7} d x}}}=\int{x^{17} d x} + {\color{red}{\frac{x^{1 + 7}}{1 + 7}}}=\int{x^{17} d x} + {\color{red}{\left(\frac{x^{8}}{8}\right)}}$$

멱법칙($$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$)을 $$$n=17$$$에 적용합니다:

$$\frac{x^{8}}{8} + {\color{red}{\int{x^{17} d x}}}=\frac{x^{8}}{8} + {\color{red}{\frac{x^{1 + 17}}{1 + 17}}}=\frac{x^{8}}{8} + {\color{red}{\left(\frac{x^{18}}{18}\right)}}$$

따라서,

$$\int{\left(x^{17} + x^{7}\right)d x} = \frac{x^{18}}{18} + \frac{x^{8}}{8}$$

적분 상수를 추가하세요:

$$\int{\left(x^{17} + x^{7}\right)d x} = \frac{x^{18}}{18} + \frac{x^{8}}{8}+C$$

$$$\int \left(x^{17} + x^{7}\right)\, dx = \left(\frac{x^{18}}{18} + \frac{x^{8}}{8}\right) + C$$$A