$$$\frac{3}{2 u}$$$의 적분

$$$\int \frac{3}{2 u}\, du$$$을(를) 구하시오.

상수배 법칙 $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$을 $$$c=\frac{3}{2}$$$와 $$$f{\left(u \right)} = \frac{1}{u}$$$에 적용하세요:

$${\color{red}{\int{\frac{3}{2 u} d u}}} = {\color{red}{\left(\frac{3 \int{\frac{1}{u} d u}}{2}\right)}}$$

$$$\frac{1}{u}$$$의 적분은 $$$\int{\frac{1}{u} d u} = \ln{\left(\left|{u}\right| \right)}$$$:

$$\frac{3 {\color{red}{\int{\frac{1}{u} d u}}}}{2} = \frac{3 {\color{red}{\ln{\left(\left|{u}\right| \right)}}}}{2}$$

따라서,

$$\int{\frac{3}{2 u} d u} = \frac{3 \ln{\left(\left|{u}\right| \right)}}{2}$$

적분 상수를 추가하세요:

$$\int{\frac{3}{2 u} d u} = \frac{3 \ln{\left(\left|{u}\right| \right)}}{2}+C$$

$$$\int \frac{3}{2 u}\, du = \frac{3 \ln\left(\left|{u}\right|\right)}{2} + C$$$A