Some Derivative-Free Quadrature Rules for Numerical Approximations of Cauchy Principal Value of Integrals

Table 1

Rules	Integral
	Approximate value of 𝐼1=𝑃∫^𝑖−𝑖((1+𝑧)𝑒^𝑧/𝑧)𝑑𝑧	Absolute error
𝑅1(𝑓)	3.575102∗𝑖	6.0×10^−6
𝑅2(𝑓)	3.575111∗𝑖	3.0×10^−6
𝑅3(𝑓)	3.575109∗𝑖	1.0×10^−6
Exact value	3.575108∗𝑖	**