Question: Maple returns unevaluated integral

I have been trying to integrate the following an expression using Maple's command PathInt:

PathInt(4*x*y*(y^4+2*x*y-2)/sqrt((1-(2*x*y)^2+(-3*y^2+1)^2)*(1+(y^2-1)^2)), [x, y] = Path(`<,>`(-(1+sqrt(2))*cos(t)-(sqrt(2)-1)*sin(t), cos(t)-sin(t)), t = 0 .. 2*Pi)).

However, Maple does not return a result, but rather an integral. Is there an alternative way to solve the integral above?

Thanks in advance.

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