Applications of complex variable residue theory for evaluating irrational definite integrals. IV (Q1330087)

[For part III see the author in ibid. 63, No. 1, 1-34 (1994; reviewed above).] Two integrals which are slight variants of the complete elliptic integrals of the first and second kind are evaluated by means of residues. An easier evaluation of a more general integral can be given by expanding the square root inside the integral by the binomial theorem and evaluating the resulting integral as a special case of the beta integral.