A closed-form model for the nonlinear interference (NLI) in Raman amplified links is presented, the formula accounts for both forward (FW) and backward (BW) pumping schemes and inter-channel stimulated Raman scattering (ISRS) effect. The formula also accounts for an arbitrary number of pumps, wavelength-dependent fibre parameters, launch-power profiles, and is tested over a distributed Raman-amplified system setup. The formula is suitable for ultra-wideband (UWB) optical transmission systems and is applied in a signal with 13~THz optical bandwidth corresponding to transmission over the S-, C-, and L- band. The accuracy of the closed-form formula is validated through comparison with numerical integration of the Gaussian noise (GN) model and split-step Fourier method (SSFM) simulations in a point-to-point transmission link.