I know that when working with real numbers, the input for a logarithm cannot be negativea, and hence when taking the integral of $\frac{1}{x}$, we take the absolute value: $$ \int{ \frac{1}{x}dx}=ln|x|+C$$
However, when I look up the integral of $\frac{1}{x ln x}$ online, I get an absolute value in the outer expression but not the inner. $$ \int{ \frac{1}{x ln x}dx}=ln| lnx|+C$$
Why isn't the inner one require an absolute value?