I hope that someone's up for the challenge; I'm attempting to solve this via computer:
\begin{equation} \int_{-\pi}^\pi{\displaystyle \frac{e^{i\cdot a\cdot t}(e^{i\cdot b\cdot t}-1)(e^{i\cdot c \cdot t}-1)}{(e^{i\cdot t}-1)(e^{i\cdot d \cdot t}+1)(e^{i\cdot f \cdot t}-1)} \dots dt} \end{equation}
I want to know if it's possible to break this up into simpler subproblems. You can use just about anything to do this, but there is one restriction. In computer science terms, I want this to be in $P$.
Let me try to explain. I don't want the work I have to do grow exponentially. For instance, if I break up the integral into two integrals, I don't want to double the amount of work I have to do. I don't want to dramatically increase the amount of work I have to do by breaking things apart, I want to keep things fairly fast.
EDIT I'd prefer to see integration techniques used for this.