I'm intested in learning how to get a sum in difference calculus. I'm willing to settle, at least for now, in learning how to integrate the following integral in calculus:
$\int(a^x(1-a^x)(1-a^x))dx$
The sum that I'm really interested in learning how to get, hopefully using difference calculus, is: $\sum_x{a^x(1-a^x)(1-a^x)}$
Even better still, extend this technique to include more $(1-a^x)$, and add limits of integration or summation.
_EDIT_
I'd like to do so without multiplying everything out, if possible