A few comments.
If you define and evaluate
i[tau_,phi_]:=Integrate[alpha E^(-t/tau)Cos[2*pi*freq*t*phi),{t,0,T}]
then Mathematica will remember that until you define something it to be something different or until you exit Mathematica. That means you do not need to type that line again.
Defining a constant, like
freq=80000000
will be remembered the same way until you change it or exit Mathematica.
The symbol Pi in Mathematica is exactly the value of pi.
If you put a ; at the end of a line it will calculate but not display the result.
Then
alpha=2;
freq=80000000;
i[tau_,phi_]:=Integrate[alpha E^(-t/tau)Cos[2*Pi*freq*t+phi],{t,0,T}];
integral=i[1,Pi/2];
Plot[integral,{T,0,6}]
will calculate the integral and then plot the function of T.
and
Plot[integral,{T,0,6},PlotPoints->500]
will do the same plot, but will calculate more points to produce a more detailed plot.
Plot will not plot expressions that contain complex numbers, even if the value is very small, and will not plot expressions that have other variables which have not been assigned a value.
Please see if this is sufficient to help you get what you are looking for.