Theoretical and indirect observational evidence suggests that the stellar initial mass function (IMF) increases with redshift. On the other hand, star formation rates (SFRs) may be as high as 100 M yr-1 in starburst galaxies. These may lead to the formation of massive clusters, hence massive stars, making the integrated galactic stellar initial mass function (IGIMF) top-heavy (i.e., the proportion of massive stars is higher than that of less massive stars). We investigate the joint effect of evolving the IMF and several measures of SFRs in dependence on the galaxywide IMF. The resulting IGIMFs have slopes α2,IGIMF in the high-mass regime, which is highly dependent on the minimum mass of the embedded cluster (Mecl,min), SFR, and mass-spectrum indices of embedded clusters (β). It is found that for z∼0-2, α2,IGIMF becomes steeper (i.e., bottom-heavy), for z∼2-4, α2,IGIMF becomes flatter (i.e., top-heavy ), and from z∼ 4 onward, α2,IGIMF again becomes steeper. The effects are faster for higher values of β. a2,IGIMF is also for higher values of Mecl,min. All of these effects may be attributable to the joint effect of increasing the temperature of the ambient medium as well as varying the SFR with increasing redshift.