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Thanks Mariusz, but this is exactly what I said I was doing in my original post. This works fine with this simple example, it's more tricky with more involved functionals.
Mathematica 12 is unable to compute: Assuming[ m > 0 && m 0 && EllipticK[m] > 0, Integrate[ ( JacobiDN[k*x, m]^2 - EllipticE[m]/EllipticK[m] )^4 , {x, -EllipticK[m]/k, EllipticK[m]/k}]] but Mathematica 11.1 can do it !? Then my...