$$$x_{0}^{4} y_{0}^{4}$$$ 关于$$$x_{0}$$$的积分
您的输入
求$$$\int x_{0}^{4} y_{0}^{4}\, dx_{0}$$$。
解答
对 $$$c=y_{0}^{4}$$$ 和 $$$f{\left(x_{0} \right)} = x_{0}^{4}$$$ 应用常数倍法则 $$$\int c f{\left(x_{0} \right)}\, dx_{0} = c \int f{\left(x_{0} \right)}\, dx_{0}$$$：
$${\color{red}{\int{x_{0}^{4} y_{0}^{4} d x_{0}}}} = {\color{red}{y_{0}^{4} \int{x_{0}^{4} d x_{0}}}}$$
应用幂法则 $$$\int x_{0}^{n}\, dx_{0} = \frac{x_{0}^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$，其中 $$$n=4$$$：
$$y_{0}^{4} {\color{red}{\int{x_{0}^{4} d x_{0}}}}=y_{0}^{4} {\color{red}{\frac{x_{0}^{1 + 4}}{1 + 4}}}=y_{0}^{4} {\color{red}{\left(\frac{x_{0}^{5}}{5}\right)}}$$
因此，
$$\int{x_{0}^{4} y_{0}^{4} d x_{0}} = \frac{x_{0}^{5} y_{0}^{4}}{5}$$
加上积分常数：
$$\int{x_{0}^{4} y_{0}^{4} d x_{0}} = \frac{x_{0}^{5} y_{0}^{4}}{5}+C$$
答案
$$$\int x_{0}^{4} y_{0}^{4}\, dx_{0} = \frac{x_{0}^{5} y_{0}^{4}}{5} + C$$$A