Evaluate: ∫ e^(tan⁻¹ x) / (1 + x²) dx
Evaluate: ∫ e^(tan⁻¹ x) / (1 + x²) dx
- A. e^(tan⁻¹ x) + C
- B. eˣ / (1 + x²) + C
- C. tan⁻¹(eˣ) + C
- D. x e^(tan⁻¹ x) + C
Answer: A) e^(tan⁻¹ x) + C
Explanation: Let tan⁻¹ x = t, then 1/(1 + x²) dx = dt. The integral becomes ∫ eᵗ dt = eᵗ + C = e^(tan⁻¹ x) + C.
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