f[x_] := (Sqrt[x + (Sqrt[x])]);

fInt[x]= Integrate[f[x], x]

fSer[x]=Normal[Series[f[x], {x, 0, 2}]]

fSerInt[x] = Integrate[fSer[x], x]

Plot[{Evaluate[fInt[x]], Evaluate[fSerInt[x]]}, {x, 0, 4},AxesLabel->{"x", "F(x)"}, PlotRange->{{0, 4},{0, 8}}, PlotLegends->{"exakt", "Reihe"}]