Partial Fractions
The integral ∫1/(x² - 1) dx can be evaluated using
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About This Question
- Subject
- mathematics
- Chapter
- integral calculus
- Topic
- partial fractions
- Difficulty
- Hard
- Year
- 2025
Solution
Correct Answer:
Partial fractions
- Identify Denominator Type: x2−1 is a factorable quadratic (x−1)(x+1).
- Decomposition Method: The integrand can be split into 'Partial Fractions':
- (x−1)(x+1)1=2(x−1)1−2(x+1)1.
- Evaluation: Integrating each simpler term yields logarithms.
- 21log∣x−1∣−21log∣x+1∣+C
- Combined Result: 21logx+1x−1+C.
This hard difficulty mathematics question is from the chapter integral calculus, covering the topic of partial fractions. It appeared in the 2025 exam.
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