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Is it always possible to explicitly evaluate $$\int\frac{1}{p(\sin{x})q(\cos{x})}dx$$ with $p(x),q(x)\in\mathbb{Q}[x] $?

gt6989b
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Lucio Tanzini
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1 Answers1

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By letting $x=2\arctan\frac{t}{2}$ your problem boils down to the integration of a rational function.
By partial fraction decomposition, such problem can be solved by locating the roots of a polynomial and their multiplicity.

Jack D'Aurizio
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