Applications of complex variable residue theory to the evaluation of irrational definite integrals. I (Q918622)

Residue theory is applied to evaluate the following four integrals \(\int^{2\pi}_{0}\cos x(a+\cos x)^{\pm 1/2}dx\) and \(\int^{2\pi}_{0}\cos x(a+\cos^ 2x)^{\pm 1/2}dx.\) Numerical results are presented. It appears that the new approach saves computational time when used instead of Simpson's numerical integration rule.