Wednesday 24 July 2013

integration - What does it mean the notation $int{Rleft( 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.

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