Find ∫ x / (x⁴ + 1) dx
Find ∫ x / (x⁴ + 1) dx
- A. (1/2) tan⁻¹(x²) + C
- B. tan⁻¹(x²) + C
- C. log(x⁴ + 1) / 4 + C
- D. x² / (x⁴ + 1) + C
Answer: A) (1/2) tan⁻¹(x²) + C
Explanation: Let x² = t, then 2x dx = dt or x dx = dt/2. Integral becomes (1/2) ∫ dt / (t² + 1) = (1/2) tan⁻¹(t) = (1/2) tan⁻¹(x²) + C.
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