Question: Integrating very large sums

A calculation I am currently doing has gotten to the stage where the time taken to integrate is just too much.
I have attached a minimal working example Maple script showing an example of the integration which is very messy. When this is run it takes ~ 10 seconds on my machine which is no issue. However the polynomial sum in this example is only a small version, and it can get, much, much larger. To the point it takes over a day to calculate (but it does evaluate).

The reason for this is that the boole integration method does not scale well with more terms in the sum. It beats the other methods for small sums (like in the example) but when the sum gets larger is not that good. The Riemann method appears to be the best for larger sums, but once again is still slow.

Is there any way to speed this up? As the Boole method is fast for this example and gives a good answer, I was thinking to break the much larger sums into smaller seperate sums and then process them all seperately with the Boole method and add up all the results?

Large_sum_integration.mw

Any feedback would be appreciated :)