Evaluate: integral of dx / (x^2 + 4x + 13).
Answer and explanation
Correct answer: C. (1/3) * arctan((x + 2) / 3) + C
- Step 1: Complete the square in denominator: x^2 + 4x + 13 = (x + 2)^2 + 9 = (x + 2)^2 + 3^2. Step 2. Standard formula: integral dx / (u^2 + a^2) = (1/a) arctan(u/a) + C. Step 3. Here u = x + 2 and a = 3: Result = (1/3) arctan((x + 2)/3) + C. *Answer: (1/3) arctan((x + 2) / 3) + C. Why not the others:** a = 3, so prefactor must be 1/3, not 1/2.
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