Evaluate: ∫ dx / (3 + 2x - x²)
Evaluate: ∫ dx / (3 + 2x - x²)
- A. (1/4) log|(x+1)/(3-x)| + C
- B. (1/4) log|(3+x)/(1-x)| + C
- C. (1/4) log|(x-3)/(x+1)| + C
- D. (1/2) log|(x+1)/(3-x)| + C
Answer: A) (1/4) log|(x+1)/(3-x)| + C
Explanation: Complete square: 3 + 2x - x² = 4 - (x-1)². Integral is ∫ dx / (2² - (x-1)²). Formula gives (1/(2*2)) log|(2+(x-1)) / (2-(x-1))| = (1/4) log|(x+1)/(3-x)| + C.
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