aa[t_]=(E^(-0.5` t) (-3.5380
18954867258
` Cos[2 t]-5.3070284323008865` Cos[t] Sin[t]) Sin[2 t]^2)/(60 Sqrt[10] \[Pi]);
bb[t_]=1-(E^(-1.` t) (-3.5380
18954867258
` Cos[2 t]-5.3070284323008865` Cos[t] Sin[t])^2 Sin[2 t]^4)/(36000 \[Pi]^2)+E^(-1.` t) (0.9782522657564643` -(1.0003421831276478` +1.
13150544600
7233`*^-19 I) E^(1.` t)+(0.06716344315861139` -4.5
13898307157
584`*^-36 I) Cos[4.` t]-(0.05519538049655178` -2.256949153578792`*^-36 I) Cos[8.` t]+(0.01012
18547091241
9` +1.
13150544600
7233`*^-19 I) Cos[12.` t]+(0.3836147080063047` -1.8055593228630336`*^-35 I) Sin[4.` t]-(0.08025174054018601` -4.5
13898307157
584`*^-36 I) Sin[8.` t]+(0.008991439618659773` +8.480665884373029`*^-20 I) Sin[12.` t]);
cc[t_]=FullSimplify[(aa[t]*aa[t])/bb[t]]
Af[t_]=Integrate[cc[\[Tau]],{\[Tau],0,t}]
Plot[Af[t],{t,0,10}]

只是画图的话，换数值积分吧