Enthalpy of Ideal Monoatomic, Diatomic and Triatomic gases

We learnt today that in ideal gases (triatomic as an eg), we can find the internal energy, and their specific heats for constant pressure and volume

u=3RT

Differentiating with Temperature

Cv= 3R

Cp= Cv+ R
= 4R

So my question is can we simply integrate this with time and then say H=4RT? And apply the same thing for the other 2 gases?