Integral of $$$\frac{1}{x \ln^{3}\left(x\right)}$$$ with respect to $$$t$$$

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

Apply the constant rule $$$\int c\, dt = c t$$$ with $$$c=\frac{1}{x \ln{\left(x \right)}^{3}}$$$:

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

Therefore,

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

Add the constant of integration:

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

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