$$$w - \frac{3}{2}$$$의 적분

$$$\int \left(w - \frac{3}{2}\right)\, dw$$$을(를) 구하시오.

각 항별로 적분하십시오:

$${\color{red}{\int{\left(w - \frac{3}{2}\right)d w}}} = {\color{red}{\left(- \int{\frac{3}{2} d w} + \int{w d w}\right)}}$$

상수 법칙 $$$\int c\, dw = c w$$$을 $$$c=\frac{3}{2}$$$에 적용하십시오:

$$\int{w d w} - {\color{red}{\int{\frac{3}{2} d w}}} = \int{w d w} - {\color{red}{\left(\frac{3 w}{2}\right)}}$$

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

$$- \frac{3 w}{2} + {\color{red}{\int{w d w}}}=- \frac{3 w}{2} + {\color{red}{\frac{w^{1 + 1}}{1 + 1}}}=- \frac{3 w}{2} + {\color{red}{\left(\frac{w^{2}}{2}\right)}}$$

따라서,

$$\int{\left(w - \frac{3}{2}\right)d w} = \frac{w^{2}}{2} - \frac{3 w}{2}$$

간단히 하시오:

$$\int{\left(w - \frac{3}{2}\right)d w} = \frac{w \left(w - 3\right)}{2}$$

적분 상수를 추가하세요:

$$\int{\left(w - \frac{3}{2}\right)d w} = \frac{w \left(w - 3\right)}{2}+C$$

$$$\int \left(w - \frac{3}{2}\right)\, dw = \frac{w \left(w - 3\right)}{2} + C$$$A