The methods for numerical calculating the Cauchy principal value integrals of the form $\ {\displaystyle\mbox{\rm v.p.} \int_{-ıfty}^{+ıfty} }og|P(ix)/Q(ix)|\,dx$ are developed, where $P(x)$ and $Q(x)$ are monic polynomials of equal degrees with integer coefficients, and $i=\sqrt{-1}$\,. These integrals play a distinguished role in theoretical chemistry.