Evaluate: ∫ (x² + 1) / (x⁴ + x² + 1) dx

Evaluate: ∫ (x² + 1) / (x⁴ + x² + 1) dx

• A. (1/√3) tan⁻¹((x² - 1) / (√3 x)) + C
• B. (1/2) log|(x² - x + 1) / (x² + x + 1)| + C
• C. tan⁻¹(x² + 1) + C
• D. (1/√3) tan⁻¹((x² + 1) / √3) + C

Answer: A) (1/√3) tan⁻¹((x² - 1) / (√3 x)) + C

Explanation: Divide by x², get ∫ (1 + 1/x²) / (x² + 1/x² + 1) dx. Let x - 1/x = t, dt = (1 + 1/x²) dx. Integral is ∫ dt / (t² + 3), resulting in (1/√3) tan⁻¹(t/√3).