Integrate the function $\frac{1}{1+\cot x}$

Question

$\begin{array}{1 1} \frac{x}{2}-\frac{1}{2} \log(\sin x+\cos x)+c \\ \frac{x}{2}+\frac{1}{2} \log(\sin x+\cos x)+c \\ \frac{x}{2}-\frac{1}{2} \log(\sin x-\cos x)+c \\ \frac{x}{2}+\frac{1}{2} \log(\sin x-\cos x)+c\end{array}$