Elliptic Integral Bug?

asked 2019-04-09 17:56:34 -0500

Julien gravatar image


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

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Typical problem with integration using maxima package abs_integrate.. Not the first one..


FrédéricC gravatar imageFrédéricC ( 2019-04-10 03:35:50 -0500 )edit