Weddle's Rule

$$\int_{x_1}^{x_{6n}} f(x)\,dx = {\textstyle{3\over 10}} h(f_1+5f_2+f_3+6f_4+5f_5+f_6+\ldots+5f_{6n-1}+f_{6n})$$

See also Bode's Rule, Hardy's Rule, Newton-Cotes Formulas, Simpson's 3/8 Rule, Simpson's Rule, Trapezoidal Rule