Question: Bug in Integration of square of Jacobi sine function

Dear all,

I believe there is a bug in integration of square of Jacobi sine function.

Here is what I did:

u := int(JacobiSN(x, k)^2, x);

The result I got is
                  x - EllipticE(JacobiSN(x, k), k)
             u := --------------------------------
However, according to  Handbook of elliptic integrals for engineers and scientists by Byrd and Friedman Eq (310.02), it is supposed to be  

                  x - EllipticE(JacobiAM(x, k), k)
             u := --------------------------------


 Note that I tried also to integrate first and third power of JacobiSN a the results are in agreement with the book.

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