Question

The value of integral $\int \frac{dx}{x(\ln x{)}^3}$ is
(where $C$ is constant of integration)

Answer 1

Put $\ln x=z\Rightarrow \frac{1}{x}dx=dz$
Now, $I=\int \frac{dz}{z^3}=-\frac{1}{2}\left(\frac{1}{z^2}\right)=\frac{-1}{2(\ln x{)}^2}+C$