 Instead, if the integrand can be written as

where is well-approximated by a low-degree polynomial, then alternative nodes formula_3 and weights formula_4 will usually give more accurate quadrature rules.These are known as Gauss-Jacobi quadrature rules, i.e.,

Common weights include formula_6 (Chebyshev–Gauss) and formula_7.One may also want to integrate over semi-infinite (Gauss-Laguerre quadrature) and infinite intervals (Gauss–Hermite quadrature).