Can Noncommutative Operators Be Integrated in Quantum Mechanics?

[mhill]

since in QM we deal with noncommutative operators , for example

$$[A,B]=i\hbar 1$$

then my question is if we could define some kind of noncommutative integral

$$\int dA dB exp(-iAB)$$ here A and B would be operators

how can you define for an operator a 'measure' $$dA$$

 

[Avodyne]

In general one never integrates over operators in QM.