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This integral is driving me nuts , anyone got a clue?

Given two real variables X and Y, one defines the function:

f(X,Y)=sqrt(a*(X+cY)^2+b*(X-cY)^2)

where a, b and c are reals and a>0, b>0.

Then the function g is defined as:

g(X,Y)=exp(-f(X,Y))

I am looking for:

1- a primitive for g

2- and/or the value of the following integrals I=integral(-infty,+infty;g(X,Y),dX) and J=integral(-infty,+infty;g(X,Y),dY).

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# Funky integral

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