# Elliptic Integral Bug?

Hi,

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

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

https://trac.sagemath.org/search?q=ab...