Indefinite Integration
Integration by Parts
Premium Question
Grade 12
Question:
$\int \frac{\ln x}{x^2} \, dx$ equals:
(1) $-\frac{\ln x + 1}{x} + C$
(2) $\frac{\ln x + 1}{x} + C$
(3) $-\frac{\ln x - 1}{x} + C$
(4) $-\frac{\ln x}{x} + C$
Step-by-Step Solution
Key Concept: Apply integration by parts with $u = \ln x$ and $dv = \frac{dx}{x^2}$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)