Indefinite Integration
Partial Fractions
Premium Question
Grade 12
Question:
If $\int \frac{dx}{x^2 - 4} = \frac{1}{k} \ln \left|\frac{x - 2}{x + 2}\right| + C$, the value of $k$ equals _____.
Step-by-Step Solution
Key Concept: Use partial fractions to write $\frac{1}{x^2 - 4} = \frac{1}{4} \left(\frac{1}{x - 2} - \frac{1}{x + 2}\right)$ before integrating term by term.
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Correct Answer: 4