$$$\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$$ 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$$$\int \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}\, dx$$$。
解答
应用常数法则 $$$\int c\, dx = c x$$$，使用 $$$c=\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$$：
$${\color{red}{\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x}}} = {\color{red}{x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}}}$$
因此，
$$\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x} = x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$
加上积分常数：
$$\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x} = x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}+C$$
答案
$$$\int \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}\, dx = x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} + C$$$A