The integral of a derivative should return the same expression, or maybe, different by adding a constant. Try something simple,

diff(2*arcsinh(x^(3/2)/sqrt(2))/3,x);

                               1/2  1/2
                              2    x
                            -------------
                                    3 1/2
                            (4 + 2 x )

int(%,x);

The answer is too long to paste, and I didn't check whether it is correct, or wrong.

Alec


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