How to integrate tanx/(x+sinx)?

I use a website called integral of the day, all the previous ones have answers, but todays I cannot ind an answer for and no online calculators can do it either.

f[up_] := NIntegrate[Tan/(x + Sin), {x, 0, up}]

Plot[f[up], {up, 0, 2}]

Even simpler integral: \int \frac{\tan (x)}{x} dx does not have finite closed-form expression in terms of very large class of special functions.