$\int \frac{d x}{1+\tan x}$ is equal to:

$\frac{x}{2}+\frac{1}{2} \log |\cos x-\sin x|+c$, C is an arbitrary constant $\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant $\frac{x}{2}-\frac{1}{2} \log |\cos x-\sin x|+c$, C is an arbitrary constant $\frac{x}{2}-\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant

$\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant

The correct answer is Option (2) → $\frac{x}{2}+\frac{1}{2} \log |\cos x+\sin x|+c$, C is an arbitrary constant