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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.

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    Have you tried standard numerical integration methods?2010-11-25
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    @Yuval:yes. They have potential; I'm not ruling them out if I can use them on subproblems. The main thing is that with these exponentials, everything seems to grow exponentially! Now I'm trying to see if breaking up the problem somehow can be competitive.2010-11-25
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    Your integrand has a number of singularities; can you guarantee that the integral is even bounded?2010-11-25
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    Yes. It's gauranteed that it will integrate to a positive integer or zero. In fact, I'd be satisfied (really elated!) if I could simply determine if the result is nonzero or not.2010-11-25
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    The singularities are worrying enough; the fact that it's oscillatory as well makes this exceedingly tough.2010-11-25
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    What does "..." mean? I'm not sure how the pattern would continue.2010-11-25
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    @Hans: From the pattern of his previous questions, he's interested in ratios of products of terms of the form $\exp(ict)-b$, where $b$ is -1, 0, or 1. So, very oscillatory and pretty damn singular.2010-11-25
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    What do you know about $a,b,c,\ldots$?2010-11-25
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    @Jonas: Integers, possibly large in absolute value.2010-11-25

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