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You need to use the so called Gauss–Jacobi quadrature with $\alpha = 0$ and $\beta = -\frac{1}{2}$. If you look at the error term, you see that you can integrate exactly for a degree up to $2n-1$ with a $n$ points scheme. EDIT to truly answer your question. You want to use this theorem about Gaussian quadrature, theorem 3.6.12 in [1] for a book reference. In ...

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