$$$n \tan{\left(x \right)} \sec{\left(x \right)}$$$ 关于$$$x$$$的积分
相关计算器: 定积分与广义积分计算器
您的输入
求$$$\int n \tan{\left(x \right)} \sec{\left(x \right)}\, dx$$$。
解答
对 $$$c=n$$$ 和 $$$f{\left(x \right)} = \tan{\left(x \right)} \sec{\left(x \right)}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{n \tan{\left(x \right)} \sec{\left(x \right)} d x}}} = {\color{red}{n \int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}}$$
$$$\tan{\left(x \right)} \sec{\left(x \right)}$$$ 的积分为 $$$\int{\tan{\left(x \right)} \sec{\left(x \right)} d x} = \sec{\left(x \right)}$$$:
$$n {\color{red}{\int{\tan{\left(x \right)} \sec{\left(x \right)} d x}}} = n {\color{red}{\sec{\left(x \right)}}}$$
因此，
$$\int{n \tan{\left(x \right)} \sec{\left(x \right)} d x} = n \sec{\left(x \right)}$$
加上积分常数：
$$\int{n \tan{\left(x \right)} \sec{\left(x \right)} d x} = n \sec{\left(x \right)}+C$$
答案
$$$\int n \tan{\left(x \right)} \sec{\left(x \right)}\, dx = n \sec{\left(x \right)} + C$$$A