Integral de $$$\frac{1}{x \ln^{3}\left(x\right)}$$$ em relação a $$$t$$$

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

Aplique a regra da constante $$$\int c\, dt = c t$$$ usando $$$c=\frac{1}{x \ln{\left(x \right)}^{3}}$$$:

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

Portanto,

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

Adicione a constante de integração:

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

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