Evaluate: ∫ dx / (x² + 6x + 13)
Evaluate: ∫ dx / (x² + 6x + 13)
- A. (1/2) tan⁻¹((x+3)/2) + C
- B. tan⁻¹((x+3)/2) + C
- C. log(x² + 6x + 13) + C
- D. 1/2 log|(x+3)/(x-3)| + C
Answer: A) (1/2) tan⁻¹((x+3)/2) + C
Explanation: Complete square: x² + 6x + 13 = (x+3)² + 4. Integral is ∫ dx / ((x+3)² + 2²) = (1/2) tan⁻¹((x+3)/2) + C.
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