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If numerical results are acceptable; Needs["NumericalCalculus`"] func[θ1_,n_]:= 1/2 ((n Cos[θ1] - 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(n Cos[θ1] + 0.2 Sqrt[1 - 25. n^2 Sin[θ1]^2])^2 + (-0.2 Cos[θ1] + n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2/(0.2 Cos[θ1] + n Sqrt[1 - 25. n^2 Sin[θ1]^2])^2) int[n_?NumberQ] := int[n] = NIntegrate[func[\[Theta]1, n], ...



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