$$$\frac{1}{x \ln^{3}\left(x\right)}$$$ 對 $$$t$$$ 的積分

求$$$\int \frac{1}{x \ln^{3}\left(x\right)}\, dt$$$。

配合 $$$c=\frac{1}{x \ln{\left(x \right)}^{3}}$$$，應用常數法則 $$$\int c\, dt = c t$$$：

$${\color{red}{\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t}}} = {\color{red}{\frac{t}{x \ln{\left(x \right)}^{3}}}}$$

因此，

$$\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t} = \frac{t}{x \ln{\left(x \right)}^{3}}$$

加上積分常數：

$$\int{\frac{1}{x \ln{\left(x \right)}^{3}} d t} = \frac{t}{x \ln{\left(x \right)}^{3}}+C$$

$$$\int \frac{1}{x \ln^{3}\left(x\right)}\, dt = \frac{t}{x \ln^{3}\left(x\right)} + C$$$A