How to Integration this function?

Is there anyway we can integrate exp(z*(z+1)/(z-1)) with respect to z?

[Sam Chak]

The function has a discontinuity at . From the plots below, the integral cannot converge in the interval

syms z

f   = exp(z*(z + 1)/(z - 1));

subplot(121)
fplot(f, [-7, 1])
xlabel('z')
title('f(z < 1)')
ylim([0, 1.2])

subplot(122)
fplot(f, [1, 3])
xlabel('z')
title('f(z > 1)')
ylim([0, 5000])

[simran]

Yes, I'm sorry I didn't mention earlier, I'm working in unit disk only, so |z|<1.

[Torsten]

If f is holomorphic in the disc |z|<=r<1, integral_{ |z|<=r } f(z) dz = pi*r^2*f(0). Then take the limit r -> 1-.