\(\int {\frac{{{e^x}\left( {1 + \sin x} \right)}}{{1 + \cos x}}} dx\) is equal to

1
\(\log \tan x + c\)
2
\({e^x}\tan \frac{x}{2} + c\)
3
\(\sin \log x + c\)
4
\({e^x} \cot x + c\)

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