This paper extends the semianalytical treatment of fast ion current density to take into account time dependence and velocity diffusion using solutions of Boltzmann's equation with a complete Coulomb collision term (Goncharov et al 2010 Phys. Plasmas17 112313). An arbitrary angle distribution of the fast ion source is assumed. The results are applicable to multi-ion-species plasma. Since analytical results provide an extra physical insight and constitute a reliable basis for verification of numerical codes, it is desirable to obtain exact solutions where possible. New results clarify the discrepancies between analytical formulae in earlier papers and contribute to the improvement of the physical basis of neutral beam injection current drive.