 Even though it does not integrate polynomials or other functions that are analytic in a large neighborhood of as well as Gauss-Legendre quadrature, Clenshaw-Curtis converges at approximately the same rate as Gauss-Legendre quadrature for most (non-analytic) integrands.Also, Clenshaw-Curtis shares the properties that Gauss-Legendre quadrature enjoys of convergence for all continuous integrands f and robustness to numerical rounding errors.Clenshaw-Curtis is straightforward to implement in formula_16 time by FFT-based methods.