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Elliptic Integral Bug?


How did Sage come up with a nice answer when being asked to compute the following elliptic integral of the second kind? $$\int \sqrt{1-(1/2)\sin^2(x)}dx$$

Using integral(f(x),x), SageMathCell returns: $$-\frac{\sqrt{2}}{48}(\sin(3x)-\sin(x))$$

Here is the link.

Is it my maths, or is it bug?

Thanks, Julien