What does it mean the notation $\int{R\left( \cos{x}, \sin{x} \right)\mathrm{d}x} $ Sometimes I find this notation and I get confused:
 $$\int{R\left( \cos{x}, \sin{x} \right)\mathrm{d}x} $$
Does it mean a rational function or taking rational operations between $\cos{x}$ and $\sin{x}$ ?
Can you explain please?
Update: I think you did not understand the question well,
Here is an example (maybe it is a lemma or a theorem):

All the integrals of the form $\int{R\left( \cos{x}, \sin{x}
 \right)\mathrm{d}x} $ can be evaluated using the substitution
  $u=\tan{\dfrac{x}{2}} $.

I think that $R$ here does not stand for a rational function but for taking rational operations(addition, subtraction, multiplication, division) between $\cos{x} $ and $\sin{x}$
Update : I did not noticed that $R$ is a rational function of two variables and that means exactly that we are taking rational operations.

In books with tables of integrals etc. (like Gradshteyn's book) $R(\cos x, \cos y)$ typically means a rational function of $(\cos x, \sin x)$. So take a rational function $R(a,b)=f^{1}(a,b)/f^{2}(a,b)$ and  plug in $a=\cos x, b=\sin x$. Here, $f^{i}(a,b), i=1,2$ are polynomials in the two variables $(a,b)$, i.e.,
$$f^{i}(a,b)=c^i_{0,0}+c^i_{1,0}a+c^i_{0,1}b+c^i_{2,0}a^2+c^i_{0,2}b^2+c^i_{1,1}ab+\dots$$
with coefficients $c^{i}_{k,l}$.
