Cannot take inverse fourier transform of a function

Question

I am trying to get the inverse fourier transform of the following function:

$$\frac{ (i*k)}{( 1 - e^{(i*k*T)} ); }$$

Where t is constant. Is there a way to approach this?

I have tried the following in MATLAB:

syms k t T
F = (i*k)/( 1 - exp(i*k*T) );
ifourier(F, k, t);

and had

ans = -(fourier(k/(exp(T*k*1i) - 1), k, -t)*1i)/(2*pi)

for some reason.

Then I tried to evaluate merely the given function

 FourierResult = fourier(k/(exp(k*1i) - 1), k, -t);

and had the same answer (matlab did not evaluate both fouriers)

is this a kind of unsolved fourier transform that no one had a solution yet? Or is there a good way to approach this?