Question: Numerical Integration very slow

I have this expression which I want to integrate numerically, but it is exponentially slow. I tried methods like _d01ajc but it does not help.

 

restart;

f2 := proc (m) options operator, arrow;

evalf(Int(exp(-(2*m-4)*exp(t)+t*(m+1))*(t-2*exp(t)), t = 0 .. infinity))

end proc;

 

plot([f2], 3 .. 10)

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