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$$$\cos{\left(1 \right)} \cos{\left(x \right)}$$$の積分
関連する計算機: 定積分・広義積分計算機
入力内容
$$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx$$$ を求めよ。
解答
定数倍の法則 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$ を、$$$c=\cos{\left(1 \right)}$$$ と $$$f{\left(x \right)} = \cos{\left(x \right)}$$$ に対して適用する:
$${\color{red}{\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x}}} = {\color{red}{\cos{\left(1 \right)} \int{\cos{\left(x \right)} d x}}}$$
余弦の積分は$$$\int{\cos{\left(x \right)} d x} = \sin{\left(x \right)}$$$:
$$\cos{\left(1 \right)} {\color{red}{\int{\cos{\left(x \right)} d x}}} = \cos{\left(1 \right)} {\color{red}{\sin{\left(x \right)}}}$$
したがって、
$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}$$
積分定数を加える:
$$\int{\cos{\left(1 \right)} \cos{\left(x \right)} d x} = \sin{\left(x \right)} \cos{\left(1 \right)}+C$$
解答
$$$\int \cos{\left(1 \right)} \cos{\left(x \right)}\, dx = \sin{\left(x \right)} \cos{\left(1 \right)} + C$$$A