Originally posted by matt grime
I'm notm sure my interpretation is correct, but in differential forms, d^2 is identically zero. so d^4(x) is zero.

d^4x is shorthand for the invariant measure in Minkowski 4 space. it is the volume 4 form, not the exterior derivative applied 4 times.
you can explicitly show that it is invariant, just by applying the change of variables formula (involving a Jacobian, as turin correctly suggests).