$$$2 \tan{\left(x \right)} \sec{\left(x \right)}$$$ 的積分
您的輸入
求$$$\int 2 \tan{\left(x \right)} \sec{\left(x \right)}\, dx$$$。
解答
套用常數倍法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$，使用 $$$c=2$$$ 與 $$$f{\left(x \right)} = \tan{\left(x \right)} \sec{\left(x \right)}$$$：
$${\color{red}{\int{2 \tan{\left(x \right)} \sec{\left(x \right)} d x}}} = {\color{red}{\left(2 \int{\tan{\left(x \right)} \sec{\left(x \right)} d x}\right)}}$$
$$$\tan{\left(x \right)} \sec{\left(x \right)}$$$ 的積分是 $$$\int{\tan{\left(x \right)} \sec{\left(x \right)} d x} = \sec{\left(x \right)}$$$：
$$2 {\color{red}{\int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}} = 2 {\color{red}{\sec{\left(x \right)}}}$$
因此，
$$\int{2 \tan{\left(x \right)} \sec{\left(x \right)} d x} = 2 \sec{\left(x \right)}$$
加上積分常數：
$$\int{2 \tan{\left(x \right)} \sec{\left(x \right)} d x} = 2 \sec{\left(x \right)}+C$$
答案
$$$\int 2 \tan{\left(x \right)} \sec{\left(x \right)}\, dx = 2 \sec{\left(x \right)} + C$$$A