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$$$\frac{\sin{\left(x \right)}}{2}$$$ 的积分
您的输入
求$$$\int \frac{\sin{\left(x \right)}}{2}\, dx$$$。
解答
对 $$$c=\frac{1}{2}$$$ 和 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{\frac{\sin{\left(x \right)}}{2} d x}}} = {\color{red}{\left(\frac{\int{\sin{\left(x \right)} d x}}{2}\right)}}$$
正弦函数的积分为 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:
$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{2} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{2}$$
因此，
$$\int{\frac{\sin{\left(x \right)}}{2} d x} = - \frac{\cos{\left(x \right)}}{2}$$
加上积分常数：
$$\int{\frac{\sin{\left(x \right)}}{2} d x} = - \frac{\cos{\left(x \right)}}{2}+C$$
答案
$$$\int \frac{\sin{\left(x \right)}}{2}\, dx = - \frac{\cos{\left(x \right)}}{2} + C$$$A