Thank you all for the replies, i try to give here a bit more information, the frequency range is lower than 1KHz, so not extrememly high, and the magnetic field calculation i want to have it in the centre of the coil/along the central axis of the coil, so not in all the space.
The fact that the current changes in time should allow me to take it outside from the integral along the coil, since it is not a function of space. But I'm not sure about this assumption, is there something I'm missing or am i correct?
Thanks