Vector-valued function with distinct singularities.
int_{0}^{1} sin(1/(x-k*omeg )) dx for k=1:.1:2 and omeg=1.1

The integrand has essential singularities
at k* 1.100 for k=1, 1.1, 1.2, ... ,2.

First we consider poles that coincide with the singularities.
The maximal number of iterations is 34.000
Estimated maximal relative error on the computed values: 2.1072805291319126e-07
Exact maximal relative error : 4.8732222225059689e-06

Next we consider a multiple pole at 1.650.
The maximal number of iterations is again 34.000
Estimated maximal relative error on the computed values: 1.8861453537907059e-14
Exact maximal relative error : 5.0421707477573066e-15