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Suppose your 3-form is tau; to extract the integrand, simply use tau[1,2,3].expr(), or tau[frame,1,2,3,chart].expr() if the vector frame and the chart are not the default ones on the manifold. Note that expr() returns a symbolic expression, which can be passed directly to integrate. For instance, for the example of question 41228, this would be

sage: tau.display(spherical.frame(), spherical)
tau = rho^2*sin(theta) drho/\dtheta/\dphi
sage: tau[spherical.frame(),1,2,3,spherical].expr()