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∫ dx / (cos x + √3 sin x) equals

1. log tan(x/2 + π/12) + C
2. log tan(x/2 - π/12) + C
3. (1/2) log tan(x/2 + π/12) + C
4. (1/2) log tan(x/2 - π/12) + C

Correct answer: (1/2) log tan(x/2 + π/12) + C

Solution

The integral simplifies to a form that involves the tangent function, and the presence of the factor of 1/2 indicates that the argument of the logarithm must be adjusted accordingly, leading to the correct option involving tan(x/2 + π/12).

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