  Theoretical and indirect observational evidences suggest that stellar initial
mass function (IMF) increases with redshift. On the other hand star formation
rates (SFR) may be as high as 100 $M_{\odot}$ yr$^{-1}$ in star burst galaxies.
These may lead to formation of massive clusters hence massive stars to make the
integrated galactic stellar initial mass function (IGIMF) top heavy (i.e.
proportion of massive stars is higher than less massive stars). We investigate
the joint effect of evolving IMF and several measures of SFR in dependence of
galaxy wide IMF. The resulting IGIMF have slopes $\alpha_{2,IGIMF}$ in the high
mass regime, which is highly dependent on the minimum mass of the embedded
cluster ($M_{ecl,min}$), star formation rates and mass spectrum indices of
embedded clusters (viz. $\beta$). It is found that for z $\sim$ 0 - 2,
$\alpha_{2,IGIMF}$ becomes steeper (i.e. bottom heavy), for z $\sim$ 2 - 4,
$\alpha_{2,IGIMF}$ becomes flatter (i.e. top heavy ) and from z $\sim$ 4
onwards $\alpha_{2,IGIMF}$ becomes again steeper. The effects are faster for
higher values of $\beta$. $\alpha_{2,IGIMF}$ is flatter also for higher values
of $M_{ecl,min}$. All these effects might be counted for the joint effect of
increasing temperature of the ambient medium as well as varying SFR with
increasing redshift.
