# How could calculate this definite integral by mathematica software

I have a expression given as $F=f_1(x)+f_2(x)+\cdots+f_N(x)$ Now I want to simplify this integral as FullSimplify[$\int \limits_0^\infty F \;dx$]. It takes along time to calculate. If I factor it into small integrals as: $\text{FullSimplify}[\int \limits_0^\infty f_1(x) \; dx] +\cdots+\text{FullSimplify}[\int \limits_0^\infty f_N(x) \; dx$]. It runs faster. Here, I want to ask that is there any function in the mathematica to factor that kind of integral. Thanks for your help.

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If the outer operation in $F$ is addition then
FullSimplify[Integrate[#, {x, 0, \[Infinity]}]] & /@ F