Further investigation shows that things work with the 
integrand defined as:

def f(t): return exp(x*exp(i*t)-v*i*t)*(exp(exp(i*t))/cosh(exp(i*t))-1)

So the source of the trouble seems to be related to the identity 

   (exp(exp(I*t))/cosh(exp(I*t))-1) = tanh(exp(I*t))

Peter

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