Integral dari $$$16 \cos{\left(x \right)} \tan{\left(x \right)}$$$

Temukan $$$\int 16 \cos{\left(x \right)} \tan{\left(x \right)}\, dx$$$.

Terapkan aturan pengali konstanta $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ dengan $$$c=16$$$ dan $$$f{\left(x \right)} = \cos{\left(x \right)} \tan{\left(x \right)}$$$:

$${\color{red}{\int{16 \cos{\left(x \right)} \tan{\left(x \right)} d x}}} = {\color{red}{\left(16 \int{\cos{\left(x \right)} \tan{\left(x \right)} d x}\right)}}$$

Sederhanakan integran:

$$16 {\color{red}{\int{\cos{\left(x \right)} \tan{\left(x \right)} d x}}} = 16 {\color{red}{\int{\sin{\left(x \right)} d x}}}$$

Integral dari sinus adalah $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$16 {\color{red}{\int{\sin{\left(x \right)} d x}}} = 16 {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$

Oleh karena itu,

$$\int{16 \cos{\left(x \right)} \tan{\left(x \right)} d x} = - 16 \cos{\left(x \right)}$$

Tambahkan konstanta integrasi:

$$\int{16 \cos{\left(x \right)} \tan{\left(x \right)} d x} = - 16 \cos{\left(x \right)}+C$$

$$$\int 16 \cos{\left(x \right)} \tan{\left(x \right)}\, dx = - 16 \cos{\left(x \right)} + C$$$A