f[x_] := (1/(1 - b (x^2)))

fint= Integrate[f[x], x]

∫f[x]\[DifferentialD]x

fint1[x_]:=fint/.b-> 1

Plot[fint1[x], {x, -1.2, 1.2}, AxesLabel->{"x", "fint1(x)"}, PlotRange->{{-1.2, 1.2},{-4, 4}}, PlotLegends->"fint1(x) = arctanh(x)"]

NIntegrate[f[x]/.b-> 1, {x, 0, (Sqrt[0.5])}]

(∫_0^(Sqrt[1/2]))f[x]\[DifferentialD]x

(∫_0^(Sqrt[1/2]))(f[x]/.b-> 1)\[DifferentialD]x

N[%]