Integrate the function $\frac{1}{1-\ tanx}$

Question

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