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Evaluate the integral: integral of 3 / (x² + 3) dx

1. sqrt(3) tan⁻¹(x/sqrt(3)) + C
2. (1/sqrt(3)) tan⁻¹(x/sqrt(3)) + C
3. 3 tan⁻¹(x/sqrt(3)) + C
4. (1/3) tan⁻¹(x/sqrt(3)) + C

Correct answer: sqrt(3) tan⁻¹(x/sqrt(3)) + C

Solution

integral of 3/(x²+3) dx = 3 * integral of 1/(x²+3) dx = 3 * (1/sqrt(3)) * tan⁻¹(x/sqrt(3)) + C = (3/sqrt(3)) tan⁻¹(x/sqrt(3)) + C = sqrt(3) tan⁻¹(x/sqrt(3)) + C.

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