$$$\frac{2 \sin{\left(x \right)}}{5}$$$의 적분

$$$\int \frac{2 \sin{\left(x \right)}}{5}\, dx$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$을 $$$c=\frac{2}{5}$$$와 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$에 적용하세요:

$${\color{red}{\int{\frac{2 \sin{\left(x \right)}}{5} d x}}} = {\color{red}{\left(\frac{2 \int{\sin{\left(x \right)} d x}}{5}\right)}}$$

사인 함수의 적분은 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$\frac{2 {\color{red}{\int{\sin{\left(x \right)} d x}}}}{5} = \frac{2 {\color{red}{\left(- \cos{\left(x \right)}\right)}}}{5}$$

따라서,

$$\int{\frac{2 \sin{\left(x \right)}}{5} d x} = - \frac{2 \cos{\left(x \right)}}{5}$$

적분 상수를 추가하세요:

$$\int{\frac{2 \sin{\left(x \right)}}{5} d x} = - \frac{2 \cos{\left(x \right)}}{5}+C$$

$$$\int \frac{2 \sin{\left(x \right)}}{5}\, dx = - \frac{2 \cos{\left(x \right)}}{5} + C$$$A