Integrate[Sinh[e z]^2/Sqrt[(a + b Sinh[e z]^2) (c + d Sinh[e z]^2)^3], z] == (Cosh[e z] (2 c - d + d Cosh[2 e z]) ((-I) a Sqrt[1 - b/a] (2 c - d + d Cosh[2 e z]) EllipticE[I ArcSinh[(Sqrt[2 - (2 b)/a] Sinh[e z])/ Sqrt[(2 a - b + b Cosh[2 e z])/a]], (b c - a d)/((-a) c + b c)] + ((-b) c + a d) Sqrt[(a Cosh[e z]^2)/(2 a - b + b Cosh[2 e z])] Sqrt[(2 a - b + b Cosh[2 e z])/a] Sqrt[(a (2 c - d + d Cosh[2 e z]))/ (c (2 a - b + b Cosh[2 e z]))] (-2 + (1/Sqrt[(c Coth[e z]^2)/(c - d)]) (Sqrt[(c (2 a - b + b Cosh[2 e z]) Csch[e z]^2)/(b c - a d)] Sqrt[(a (2 c - d + d Cosh[2 e z]) Csch[e z]^2)/((-b) c + a d)] EllipticF[ArcSin[Sqrt[(a (2 c - d + d Cosh[2 e z]) Csch[e z]^2)/ (-2 b c + 2 a d)]], (b c - a d)/(a c - a d)])) Sinh[e z]))/ (4 (c - d) (b c - a d) e Sqrt[(a Cosh[e z]^2)/(2 a - b + b Cosh[2 e z])] Sqrt[(2 a - b + b Cosh[2 e z])/a] Sqrt[(a (2 c - d + d Cosh[2 e z]))/ (c (2 a - b + b Cosh[2 e z]))] Sqrt[(a + b Sinh[e z]^2) (c + d Sinh[e z]^2)^3])

Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"], SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], "3"]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", SqrtBox[RowBox[List["1", "-", FractionBox["b", "a"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", "b"]], "a"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]], SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "c"]], "+", RowBox[List["b", " ", "c"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List[FractionBox["1", SqrtBox[FractionBox[RowBox[List["c", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List["c", "-", "d"]]]]], RowBox[List["(", RowBox[List[SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]]]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]]]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "c"]], "+", RowBox[List["2", " ", "a", " ", "d"]]]]]], "]"]], ",", FractionBox[RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], RowBox[List[RowBox[List["a", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]]]]], "]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], ")"]], " ", "e", " ", SqrtBox[FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], "3"]]]]]], ")"]]]]]]]]

<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> &#8747; </mo> <mrow> <mfrac> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> a </mi> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <msqrt> <mfrac> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> coth </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> c </mi> <mo> - </mo> <mi> d </mi> </mrow> </mfrac> </msqrt> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mfrac> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> F </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <msup> <mi> sin </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> csch </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mrow> <mrow> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> b </mi> <mi> a </mi> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> E </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <msqrt> <mrow> <mn> 2 </mn> <mo> - </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mi> a </mi> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <msqrt> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> a </mi> </mfrac> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mrow> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> c </mi> <mo> - </mo> <mi> d </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mi> d </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cosh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mi> a </mi> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> c </mi> </mrow> <mo> - </mo> <mi> d </mi> <mo> + </mo> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mi> c </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> d </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sinh </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mn> 3 </mn> </msup> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> d </ci> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> c </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <cosh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <cosh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <power /> <apply> <coth /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> EllipticF </ci> <apply> <arcsin /> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <csch /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -2 </cn> </apply> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> a </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <ci> EllipticE </ci> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> c </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> b </ci> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <ci> d </ci> </apply> </apply> </apply> <ci> e </ci> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <cosh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <ci> d </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <ci> c </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> <apply> <times /> <ci> b </ci> <apply> <cosh /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> a </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> d </ci> <apply> <power /> <apply> <sinh /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <ci> c </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"], SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c_", "+", RowBox[List["d_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]], ")"]], "3"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", SqrtBox[RowBox[List["1", "-", FractionBox["b", "a"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", FractionBox[RowBox[List[SqrtBox[RowBox[List["2", "-", FractionBox[RowBox[List["2", " ", "b"]], "a"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]], SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "c"]], "+", RowBox[List["b", " ", "c"]]]]]]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", FractionBox[RowBox[List[SqrtBox[FractionBox[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]]]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "b"]], " ", "c"]], "+", RowBox[List["a", " ", "d"]]]]]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["ArcSin", "[", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Csch", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "b", " ", "c"]], "+", RowBox[List["2", " ", "a", " ", "d"]]]]]], "]"]], ",", FractionBox[RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], RowBox[List[RowBox[List["a", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]]]]], "]"]]]], SqrtBox[FractionBox[RowBox[List["c", " ", SuperscriptBox[RowBox[List["Coth", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List["c", "-", "d"]]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "-", "d"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "c"]], "-", RowBox[List["a", " ", "d"]]]], ")"]], " ", "e", " ", SqrtBox[FractionBox[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Cosh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]], " ", SqrtBox[FractionBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], "a"]], " ", SqrtBox[FractionBox[RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "c"]], "-", "d", "+", RowBox[List["d", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]]]]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", RowBox[List["d", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], "3"]]]]]]]]]]]

2002-12-18