A method is described for evaluating integrals of the form "formula" which arise in treating certain statistical mechanical models by means of the Bethe ansatz (quantum inverse scattering) technique. We specify which integrals of this class can be expressed in closed form, along with their values and evaluate some generalizations.
Glasser, M. L., & Boersma, J. (1999). A class of integrals associated with the Bethe ansatz. Journal of Physics A: Mathematical and General, 32(47), 8261-8264. https://doi.org/10.1088/0305-4470/32/47/305