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\[Lambda]\))\)\ v0\^2\ \[Lambda]\^2\)\)\) - \(E\^\(2\ v0\ \((\(-r\) + v0)\)\ \[Lambda]\)\ \((1 - v0\^2\ \[Lambda]\ \((2 + r\^2\ \[Lambda])\) + r\^2\ v0\^2\ \[Lambda]\^2\ Cos[2\ ArcCos[v0\/r]]) \)\)\/\(2\ \((\(-1\) + E\^\(2\ v0\ \((\(-r\) + v0)\)\ \[Lambda]\)) \)\ v0\^2\ \[Lambda]\^2\))\), {r, v0 + small, v0 + 5}] \ ; \n\nEpra[\[Lambda]_] := NIntegrate[ n0[r]\ \(( E\^\(2\ v0\ \((\(-r\) + v0)\)\ \[Lambda]\)\/\(2\ \((\(-1\) + E\^\(2\ v0\ \((\(-r\) + v0)\)\ \[Lambda]\)) \)\ v0\^2\ \[Lambda]\^2\) - \(1 + 2\ v0\^2\ \[Lambda] + 2\ r\^2\ v0\^2\ \[Lambda]\^2 + 2\ v0\^4\ \[Lambda]\^2 - 2\ r\ v0\ \[Lambda]\ \((1 + 2\ v0\^2\ \[Lambda])\)\)\/\(2 \ \((\(-1\) + E\^\(2\ v0\ \((\(-r\) + v0)\)\ \[Lambda]\)) \)\ v0\^2\ \[Lambda]\^2\))\), {r, v0 + small, v0 + 5}] \ ; \ntoSolve[\[Lambda]_] := Etotal[\[Lambda]] - E0; \n small\ = \ 0.001\ ; \), "\n"}]], "Input"], Cell[BoxData[ RowBox[{"(*", " ", RowBox[{"formula", "\n", "\n", RowBox[{\(\[Integral]\_0\%\(ArcCos[v0/r]\)\), RowBox[{ \((r\^2 + v0\^2 - \ 2\ r\ 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