Using partial fractions, ∫(dx)/(x² − 1) equals:
Using partial fractions, ∫(dx)/(x² − 1) equals:
- A. (1/2)ln|(x−1)/(x+1)| + C
- B. ln|(x−1)/(x+1)| + C
- C. tan⁻¹x + C
- D. (1/2)ln|(x+1)/(x−1)| + C
Answer: A) (1/2)ln|(x−1)/(x+1)| + C
Explanation: 1/(x²−1) = 1/[(x−1)(x+1)] = A/(x−1) + B/(x+1). Solving: A=1/2, B=−1/2. Integral = (1/2)ln|x−1| − (1/2)ln|x+1| + C = (1/2)ln|(x−1)/(x+1)| + C.
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