Integral dari $$$\frac{\cos{\left(u \right)}}{v}$$$ terhadap $$$u$$$

Temukan $$$\int \frac{\cos{\left(u \right)}}{v}\, du$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(u \right)}\, du = c \int f{\left(u \right)}\, du$$$ dengan $$$c=\frac{1}{v}$$$ dan $$$f{\left(u \right)} = \cos{\left(u \right)}$$$:

$${\color{red}{\int{\frac{\cos{\left(u \right)}}{v} d u}}} = {\color{red}{\frac{\int{\cos{\left(u \right)} d u}}{v}}}$$

Integral dari kosinus adalah $$$\int{\cos{\left(u \right)} d u} = \sin{\left(u \right)}$$$:

$$\frac{{\color{red}{\int{\cos{\left(u \right)} d u}}}}{v} = \frac{{\color{red}{\sin{\left(u \right)}}}}{v}$$

Oleh karena itu,

$$\int{\frac{\cos{\left(u \right)}}{v} d u} = \frac{\sin{\left(u \right)}}{v}$$

Tambahkan konstanta integrasi:

$$\int{\frac{\cos{\left(u \right)}}{v} d u} = \frac{\sin{\left(u \right)}}{v}+C$$

$$$\int \frac{\cos{\left(u \right)}}{v}\, du = \frac{\sin{\left(u \right)}}{v} + C$$$A