  An analytical-numeric calculation method of extremely complicated integrals
is presented. These integrals appear often in magnet soliton theory. The
appropriate analytical continuation and a corresponding integration contour
allow to reduce the calculation of wide class of integrals to a numeric search
of integrand denominator roots (in a complex plane) and a subsequent residue
calculations. The acceleration of series convergence of residue sum allows to
reach the high relative accuracy limited only by roundoff error in case when
$10\div 15$ terms are taken into account. The circumscribed algorithm is
realized in the C program and tested on the example allowing analytical
solution. The program was also used to calculate some typical integrals that
can not be expressed through elementary functions. In this case the control of
calculation accuracy was made by means of one-dimensional numerical integration
procedure.
