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$$$\frac{9}{949 x^{4}}$$$ 的积分
您的输入
求$$$\int \frac{9}{949 x^{4}}\, dx$$$。
解答
对 $$$c=\frac{9}{949}$$$ 和 $$$f{\left(x \right)} = \frac{1}{x^{4}}$$$ 应用常数倍法则 $$$\int c f{\left(x \right)}\, dx = c \int f{\left(x \right)}\, dx$$$：
$${\color{red}{\int{\frac{9}{949 x^{4}} d x}}} = {\color{red}{\left(\frac{9 \int{\frac{1}{x^{4}} d x}}{949}\right)}}$$
应用幂法则 $$$\int x^{n}\, dx = \frac{x^{n + 1}}{n + 1}$$$ $$$\left(n \neq -1 \right)$$$，其中 $$$n=-4$$$：
$$\frac{9 {\color{red}{\int{\frac{1}{x^{4}} d x}}}}{949}=\frac{9 {\color{red}{\int{x^{-4} d x}}}}{949}=\frac{9 {\color{red}{\frac{x^{-4 + 1}}{-4 + 1}}}}{949}=\frac{9 {\color{red}{\left(- \frac{x^{-3}}{3}\right)}}}{949}=\frac{9 {\color{red}{\left(- \frac{1}{3 x^{3}}\right)}}}{949}$$
因此，
$$\int{\frac{9}{949 x^{4}} d x} = - \frac{3}{949 x^{3}}$$
加上积分常数：
$$\int{\frac{9}{949 x^{4}} d x} = - \frac{3}{949 x^{3}}+C$$
答案
$$$\int \frac{9}{949 x^{4}}\, dx = - \frac{3}{949 x^{3}} + C$$$A