Numerical integral using conditionally different functions for the same interval

I want to integrate a function from -Inf to +Inf using complex plane with a deformred path to avoid the branch cut of square root function.

Ixx = @(Nu) (1/(4 .* pi^2) .* omega .* mu) .* pi/2 .* (2.*k0^2 - Nu.^2)/kz(Nu) .* I2(Nu) .* I2_2(Nu);

wpoints = [(-1-1j).*del, (1+1j).*del];

Exx = integral(Ixx, -100*beta_rhop, 100*beta_rhop, 'Waypoints', wpoints);

In the numerical integral of this kind (with a complex path of integration) I don't have any control on the independant variable. I want to use a different set of functions instead of I2(Nu) and I2_2(Nu) when beta_rhop == |Nu| . In other words, I want to use Ixx as a discontinuous function at points when beta_rhop = |Nu| . Is this possible?