New Derivative Based Open Newton-Cotes Quadrature Rules

Table 7

Computational cost for evaluating ∫¹₀(𝑥ln(1+𝑥)/(1+𝑥²))𝑑𝑥.

Formula	Order	𝑁	FE in composite form	DE in composite form	Total
ONC
𝑛=0	2	18258	9129	0	9129
𝑛=1	2	22362	14908	0	14908
𝑛=2	4	188	141	0	141
𝑛=3	4	215	172	0	172
𝑛=4	6	60	50	0	50
ONC2
𝑛=0	4	134	67	2	69
𝑛=1	6	33	22	24	46
𝑛=2	8	20	15	12	27
𝑛=3	10	15	12	14	26
𝑛=4	12	18	15	14	29
ONC4
𝑛=0	4	134	67	2	69
𝑛=1	4	174	116	2	118
𝑛=2	6	40	30	2	32
𝑛=3	6	50	40	2	42
𝑛=4	8	24	20	2	22