Evaluate ∫(x² + 1)/(x² − 1) dx.
Evaluate ∫(x² + 1)/(x² − 1) dx.
- A. x + ln|(x−1)/(x+1)| + C
- B. x − ln|x²−1| + C
- C. x + ln|x²−1| + C
- D. x + (1/2)ln|(x−1)/(x+1)| + C
Answer: A) x + ln|(x−1)/(x+1)| + C
Explanation: (x²+1)/(x²−1) = 1 + 2/(x²−1). ∫1 dx + 2∫dx/(x²−1) = x + 2[(1/2)ln|(x−1)/(x+1)|] + C = x + ln|(x−1)/(x+1)| + C.
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