Evaluate: ∫ dx / (x(x³ + 1))
Evaluate: ∫ dx / (x(x³ + 1))
- A. (1/3) log|x³ / (x³ + 1)| + C
- B. log|x / (x³ + 1)| + C
- C. (1/3) log|(x³ + 1) / x³| + C
- D. log|(x³+1)/x| + C
Answer: A) (1/3) log|x³ / (x³ + 1)| + C
Explanation: Multiply numerator and denominator by x²: ∫ x² dx / (x³(x³ + 1)). Let x³ = t, 3x² dx = dt. (1/3) ∫ dt / (t(t+1)) = (1/3) log|t/(t+1)|.
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