Problem: Compute $$\int_0^{12\pi} dx \frac{x}{6+\cos 8x}$$ It looks like the OP is trying to compute the antiderivative and use the fundamental theorem of calculus. With multiple periods, that approach is paved with all sorts of difficulty that is really an artifice related to the functional form of the antiderivative. In truth, there should be no […]

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