$$$\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$$ 對 $$$x$$$ 的積分
相關計算器: 定積分與廣義積分計算器
您的輸入
求$$$\int \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}\, dx$$$。
解答
配合 $$$c=\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$$，應用常數法則 $$$\int c\, dx = c x$$$：
$${\color{red}{\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x}}} = {\color{red}{x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}}}$$
因此，
$$\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x} = x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}$$
加上積分常數：
$$\int{\left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)} d x} = x \left(y - \sin{\left(y \right)}\right) \cos{\left(y \right)}+C$$
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