Use a Trigonometric Substitution to Evaluate the Integral $$\int \frac { d x } { x \left( 1 + 4 \ln ^ { 2 } x \right) }$$

Multiple Choice

Use a trigonometric substitution to evaluate the integral.
- $$\int \frac { d x } { x \left( 1 + 4 \ln ^ { 2 } x \right) }$$

A) $\frac { 1 } { 2 x } \tan ^ { - 1 } ( 2 \ln x ) + C$
B) $\frac { 1 } { 8 } \ln \left( 1 + 4 \ln ^ { 2 } x \right) + C$
C) $\frac { 1 } { 2 } \tan ^ { - 1 } ( 2 \ln x ) + C$
D) $\frac { 1 } { 2 } \tan ^ { - 1 } \left( 4 \ln ^ { 2 } x \right) + C$