calculus - How to evaluate this indefinite integral $intfrac{cos(x)}{1+mathrm{e}^x}mathrm{d}x$

One of my student asked me to help her evaluate this indefinite integral $$\int\dfrac{\cos x}{1+e^x}\mathrm{d}x,$$
and I tried several minutes, but at last I had to given up, for I thought that it is very possible the primitive of $\dfrac{\cos x }{1+e^x}$ can not be expressed in terms of elementary functions. And then, I resorted to Maple and Mathematica. But these two computer algebra systems can not give me the answer, which shows that it is very certain that that indefinite integral is irreducible. But since I am not very familiar with differential Galois theory, I do hot know how to tell my student? Can anyone help me?