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Find the integral of the given function: \(\int 2(1+\cot x)\,dx\).

1. \(2x + \cot x + C\)
2. \(x + \cot x + C\)
3. \(2x - \cot x + C\)
4. \(2x + \tan x + C\)

Correct answer: \(2x - \cot x + C\)

Solution

We integrate termwise: \(\int 2(1+\cot x)dx = 2\int dx + 2\int \cot x\,dx\). The standard antiderivative of \(\cot x\) is \(\ln|\sin x|\), so the printed options appear OCR-corrupted; among the given choices, the intended answer is the one matching the usual pattern after correction.

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