Verify the Integration Formula $$\int \frac { \tanh ^ { - 1 } ( \ln x ) } { x } d x = \ln x \tanh ^ { - 1 } ( \ln x ) + \frac { 1 } { 2 } \ln \left( 1 - ( \ln x ) ^ { 2 } \right) + C$$

Verify the integration formula.
- $$\int \frac { \tanh ^ { - 1 } ( \ln x ) } { x } d x = \ln x \tanh ^ { - 1 } ( \ln x ) + \frac { 1 } { 2 } \ln \left( 1 - ( \ln x ) ^ { 2 } \right) + C$$