One multiple complex conjugate pair of poles \pm i*B 
int_{0}^{1} sinh( 1/(x^2+B^2) ) dx

Pole is +/- 1.000i
The maximal number of iterations is 17.000
Computed value: 8.7974890970966702e-01
Estimated relative error : 2.5239543064430737e-16
Exact relative error : 2.2204460492503131e-16

Pole is +/- 2.000i
The maximal number of iterations is 17.000
Computed value: 2.3393310806757550e-01
Estimated relative error : 7.1188492757368705e-16
Exact relative error : 2.2204460492503131e-16

Pole is +/- 3.000i
The maximal number of iterations is 17.000
Computed value: 1.0745651578818866e-01
Estimated relative error : 3.8744382430478546e-16
Exact relative error : 2.2204460492503131e-16

Pole is +/- 4.000i
The maximal number of iterations is 17.000
Computed value: 6.1282997467641001e-02
Estimated relative error : 0.0000000000000000e+00
Exact relative error : 1.1102230246251565e-16

Pole is +/- 5.000i
The maximal number of iterations is 17.000
Computed value: 3.9489372318567174e-02
Estimated relative error : 0.0000000000000000e+00
Exact relative error : 2.2204460492503131e-16

Pole is +/- 6.000i
The maximal number of iterations is 17.000
Computed value: 2.7528255918594046e-02
Estimated relative error : 1.2603221076603568e-16
Exact relative error : 2.2204460492503131e-16

Pole is +/- 7.000i
The maximal number of iterations is 17.000
Computed value: 2.0272396252557931e-02
Estimated relative error : 0.0000000000000000e+00
Exact relative error : 0.0000000000000000e+00

Pole is +/- 8.000i
The maximal number of iterations is 17.000
Computed value: 1.5545000357541633e-02
Estimated relative error : 6.6956195667189238e-15
Exact relative error : 3.3306690738754696e-16

Pole is +/- 9.000i
The maximal number of iterations is 17.000
Computed value: 1.2295556596944791e-02
Estimated relative error : 2.1162809454366455e-15
Exact relative error : 2.2204460492503131e-16

Pole is +/- 10.000i
The maximal number of iterations is 17.000
Computed value: 9.9670302697005449e-03
Estimated relative error : 6.9618469254590761e-16
Exact relative error : 2.2204460492503131e-16