$$$\frac{\sin{\left(x \right)}}{a}$$$ 关于$$$x$$$的积分

求$$$\int \frac{\sin{\left(x \right)}}{a}\, dx$$$。

对 $$$c=\frac{1}{a}$$$ 和 $$$f{\left(x \right)} = \sin{\left(x \right)}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：

$${\color{red}{\int{\frac{\sin{\left(x \right)}}{a} d x}}} = {\color{red}{\frac{\int{\sin{\left(x \right)} d x}}{a}}}$$

正弦函数的积分为 $$$\int{\sin{\left(x \right)} d x} = - \cos{\left(x \right)}$$$:

$$\frac{{\color{red}{\int{\sin{\left(x \right)} d x}}}}{a} = \frac{{\color{red}{\left(- \cos{\left(x \right)}\right)}}}{a}$$

因此，

$$\int{\frac{\sin{\left(x \right)}}{a} d x} = - \frac{\cos{\left(x \right)}}{a}$$

加上积分常数：

$$\int{\frac{\sin{\left(x \right)}}{a} d x} = - \frac{\cos{\left(x \right)}}{a}+C$$

$$$\int \frac{\sin{\left(x \right)}}{a}\, dx = - \frac{\cos{\left(x \right)}}{a} + C$$$A