Evaluate $\int \left( \ln(\ln x^2) + \frac{2}{\ln x^2} \right) dx$
Step-by-Step Solution
Key Concept: General
$\int \left( \ln(\ln x^2) + \frac{2}{\ln x^2} \right) dx = \int \left( \underbrace{\ln(2 \ln x)}_{f(x)} + \underbrace{x \left( \frac{1}{2 \ln x} \cdot \frac{2}{x} \right)}_{f'(x)} \right) dx = x \ln(\ln x^2) + C$
Correct Answer: $x \ln(\ln x^2) + C$