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$$$\cos{\left(1 \right)} \cos{\left(x \right)}$$$ 的積分
您的輸入
求$$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx$$$。
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 $$$c=\cos{\left(1 \right)}$$$ 與 $$$f{\left(x \right)} = \cos{\left(x \right)}$$$：
$${\color{red}{\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x}}} = {\color{red}{\cos{\left(1 \right)} \int{\cos{\left(x \right)} d x}}}$$
餘弦函數的積分為 $$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$：
$$\cos{\left(1 \right)} {\color{red}{\int{\cos{\left(x \right)} d x}}} = \cos{\left(1 \right)} {\color{red}{\sin{\left(x \right)}}}$$
因此，
$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}$$
加上積分常數：
$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}+C$$
答案
$$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx = \sin{\left(x \right)} \cos{\left(1 \right)} + C$$$A