The conditions that affect the formation of stars in radiatively and mechanically active environments are quite different than the conditions that apply to our local interstellar neighborhood. In such galactic environments, a variety of feedback processes can play a significant role in shaping the initial mass function (IMF). Here, we present a numerical study on the effects of an accreting black hole and the influence of nearby massive stars to a collapsing, 800 M_sun, molecular cloud at 10 pc distance from the black hole. We parametrize and study radiative feedback effects of hard X-rays emanating from the black hole broad line region, increased cosmic ray rates due to supernovae in starbursts, and strong UV radiation produced by nearby massive stars. We also investigate the importance of shear from the supermassive, 10^6-10^8 M_sun, black hole as the star-forming cloud orbits around it. We find that thermal pressure from X-rays compresses the cloud, which induces a high star formation rate early on, but reduces the overall star formation efficiency to about 7% due to gas depletion by evaporation. We see that the turn-over mass of the IMF increases up to a factor of 2.3, M_turn = 1-1.5 M_sun, for the model with the highest X-ray flux (160 erg s^-1 cm^-2), while the high-mass slope of the IMF becomes Gamma > -1. This results in more high mass stars and a non-Salpeter IMF. Cosmic rays penetrate deeply into the cloud and increase the gas temperature (50-200 K), which leads to a reduced formation efficiency of low mass stars. High cosmic ray rates increase the average mass of stars, thereby shifting the turn-over mass to higher values, i.e., up to several solar masses. Due to this process, the onset of star formation is also delayed. We conclude that the IMF inside active galaxies is different than the one obtained from local environments.