$$$\sin{\left(x \right)} \cos{\left(2 \right)}$$$ 的积分
您的输入
求$$$\int \sin{\left(x \right)} \cos{\left(2 \right)}\, dx$$$。
解答
对 $$$c=\cos{\left(2 \right)}$$$ 和 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x}}} = {\color{red}{\cos{\left(2 \right)} \int{\sin{\left(x \right)} d x}}}$$
正弦函数的积分为 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$\cos{\left(2 \right)} {\color{red}{\int{\sin{\left(x \right)} d x}}} = \cos{\left(2 \right)} {\color{red}{\left(- \cos{\left(x \right)}\right)}}$$
因此，
$$\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x} = - \cos{\left(2 \right)} \cos{\left(x \right)}$$
加上积分常数：
$$\int{\sin{\left(x \right)} \cos{\left(2 \right)} d x} = - \cos{\left(2 \right)} \cos{\left(x \right)}+C$$
答案
$$$\int \sin{\left(x \right)} \cos{\left(2 \right)}\, dx = - \cos{\left(2 \right)} \cos{\left(x \right)} + C$$$A