A Note on Finite Quadrature Rules with a Kind of Freud Weight Function

Table 1

∫^+∞_−∞𝑥⁻⁶exp(−1/𝑥²)𝑓(𝑥)𝑑𝑥.

𝑓(𝑥)	Approx. value (2-point)	Exact value	Error
cos𝑥	0.9103037512	0.9382539141	0.0279501629
exp(−2/𝑥^2)	0.0661839608	0.0852772257	0.0190932649
exp(−cos𝑥)	0.6702559297	0.6812645398	0.0110086101