The integral ∫(x dx)/(x² + 1)² equals:
The integral ∫(x dx)/(x² + 1)² equals:
- A. −1/[2(x²+1)] + C
- B. 1/[2(x²+1)] + C
- C. ln(x²+1) + C
- D. tan⁻¹x + C
Answer: A) −1/[2(x²+1)] + C
Explanation: Let u = x²+1, du = 2x dx → x dx = du/2. ∫(du/2)/u² = (1/2)∫u⁻² du = (1/2)(−1/u) + C = −1/[2(x²+1)] + C.
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