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Completing the square in x² + 2x + 5 helps integrate its reciprocal. The result is
Aln(x² + 2x + 5) + C
B2 tan⁻¹((x + 1)/2) + C
C(1/2) tan⁻¹((x + 1)/2) + C
D(1/2) tan⁻¹(x + 1) + C
Answer & Solution
Correct answer: C. (1/2) tan⁻¹((x + 1)/2) + C
Completing the square gives (x + 1)² + 4, so the integral is (1/2)tan⁻¹((x + 1)/2).
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