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$$$\frac{\sin{\left(x \right)}}{23}$$$ 的積分
您的輸入
求$$$\int \frac{\sin{\left(x \right)}}{23}\, dx$$$。
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 $$$c=\frac{1}{23}$$$ 與 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$：
$${\color{red}{\int{\frac{\sin{\left(x \right)}}{23} d x}}} = {\color{red}{\left(\frac{\int{\sin{\left(x \right)} d x}}{23}\right)}}$$
正弦函數的積分為 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$：
$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{23} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{23}$$
因此，
$$\int{\frac{\sin{\left(x \right)}}{23} d x} = - \frac{\cos{\left(x \right)}}{23}$$
加上積分常數：
$$\int{\frac{\sin{\left(x \right)}}{23} d x} = - \frac{\cos{\left(x \right)}}{23}+C$$
答案
$$$\int \frac{\sin{\left(x \right)}}{23}\, dx = - \frac{\cos{\left(x \right)}}{23} + C$$$A