# Integration in Sage

Hi,

I am working on a problem in Lattice theory where I have to integrate polynomials with thousands of terms. And the integration is in 8 dimensions (means its not a single integral but 8 integrals). I am using integral() in sage to integrate the polynomials. It takes too much time to integrate the polynomials. Is there any way to speed up this integration in sage?

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I don't know all the details of what you are doing. However, since you are working with polynomials, you might be able to define a map that gives you the integral directly without calling Sage's integration. For $p(x) = \sum_{n=0}^N a_n x^n$, an antiderivative is $P(x) = P_0+\sum_{n=0}^N a_n \frac{x^{n+1}}{n+1}$. So, you can define a Sage function that extracts the coefficients and then produces the antiderivative.

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