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The problem does not come from the plotting function but from the fact that your functions FF1, FF2, FF3 cannot return numerical values because Phi_1, Phi_2 and Phi_3 contain unevaluated integrals:

Phi_1
-2*integrate((w^2 - 1)/sqrt((4*w^6 + 7*sqrt(2)*w^3 - 4)*w), w)

You should probably use numerical_integral instead of integrate and specify some integration bounds.

The case of the commented line worked because SageMath was capable to find an explicit primitive:

R=-I*w^2
Phi_1=((1-w^2)/R).integrate(w)
Phi_1
-I*w - I/w