$$$- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}$$$ 的積分
相關計算器: 定積分與廣義積分計算器
您的輸入
求$$$\int \left(- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}\right)\, dx$$$。
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 $$$c=- \tan{\left(1 \right)}$$$ 與 $$$f{\left(x \right)} = \tan{\left(x \right)} \sec{\left(x \right)}$$$：
$${\color{red}{\int{\left(- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}\right)d x}}} = {\color{red}{\left(- \tan{\left(1 \right)} \int{\tan{\left(x \right)} \sec{\left(x \right)} d x}\right)}}$$
$$$\tan{\left(x \right)} \sec{\left(x \right)}$$$ 的積分是 $$$\int{\tan{\left(x \right)} \sec{\left(x \right)} d x} = \sec{\left(x \right)}$$$：
$$- \tan{\left(1 \right)} {\color{red}{\int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}} = - \tan{\left(1 \right)} {\color{red}{\sec{\left(x \right)}}}$$
因此，
$$\int{\left(- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}\right)d x} = - \tan{\left(1 \right)} \sec{\left(x \right)}$$
加上積分常數：
$$\int{\left(- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}\right)d x} = - \tan{\left(1 \right)} \sec{\left(x \right)}+C$$
答案
$$$\int \left(- \tan{\left(1 \right)} \tan{\left(x \right)} \sec{\left(x \right)}\right)\, dx = - \tan{\left(1 \right)} \sec{\left(x \right)} + C$$$A