I don't understand the following behavior of Integrate. The function to be integrated is real and continuous over the domain of integration, but the result provided by Integrate is not real. A branch cut problem in Integrate's implementation?
Many similar integrands seem to fail in the same way, and the solutions provided by Mathematica for more general elliptic integrals (where the parameters and bounds of integration are variables rather than specific integers) also seem to fail.
Hopefully someone here knows what the issue is. (This is the student version of Mathematica 18.104.22.168.)