Integrate $\int \frac{1}{1+ \tan x}dx$ Does this integral have a closed form?
$$\int \frac{1}{1+ \tan x}\,dx$$
My attempt:
$$\int \frac{1}{1+ \tan x}\,dx=\ln (\sin x + \cos x) +\int \frac{\tan x}{1+ \tan x}\,dx$$
What is next?

Notice that $$\int \frac{\tan{x}}{1+\tan{x}}= \int 1-\frac{1}{1+\tan{x}}$$
