Definite Integrals, Some Involving Residue Theory Evaluated by Maple Code

The calculus of residue is applied to evaluate certain integrals in the range (-{infinity} to {infinity}) using the Maple symbolic code. These integrals are of the form {integral}{sub -{infinity}}{sup {infinity}} cos(x)/[(x{sup 2} + a{sup 2})(x{sup 2} + b{sup 2}) (x{sup 2} + c{sup 2})]dx and similar extensions. The Maple code is also applied to expressions in maximum likelihood estimator moments when sampling from the negative binomial distribution. In general the Maple code approach to the integrals gives correct answers to specified decimal places, but the symbolic result may be extremely long and complex.