By generalizing the methods for double and triple integration, I have prepared a set of rules for integration over m variables. This technique may find applications in analyzing high-dimensional networks of spiking neurons, in quantum mechanics, and elsewhere.

• Linearity holds for m-dimensional integrals, allowing the rules for integrating various functions to be combined.
• The rules for m-dimensional integrals will hold for infinite-dimensional integrals.
• Below, rules for computing m-dimensional polynomial functions, product functions, and sums of exponential functions are given. 

• Some special cases of the above rules are given next to simplify calculations under these particular conditions.