Wolfram Researchfunctions.wolfram.comOther Wolfram Sites
Search Site
Function CategoriesGraphics GalleryNotationsGeneral IdentitiesAbout This Site Email Comments

View Related Information In
The Documentation Center
MathWorld

Download All Formulas For This Function
Mathematica Notebook
PDF File

Download All Introductions For This Function
Mathematica Notebook
PDF File

 

Developed with Mathematica -- Download a Free Trial Version
 











Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function and trigonometric functions > Involving algebraic functions of the direct function and trigonometric functions > Involving algebraic functions of sin > Involving (a sin2(e z)+b cos2(e z))beta





http://functions.wolfram.com/01.07.21.2392.01









  


  










Input Form





Integrate[(a Sin[e z]^2 + b Cos[e z]^2)^(5/2), z] == (1/e) ((1/(60 Sqrt[2])) ((a - b) (-11 (a + b) + 3 (a - b) Cos[2 e z]) Sqrt[a + b + (-a + b) Cos[2 e z]] Sin[2 e z])) + (1/(15 Sqrt[2] e)) (-(4 I (8 a^3 + 7 a^2 b + 7 a b^2 + 8 b^3) Sqrt[a + b + (-a + b) Cos[2 e z]] Sqrt[(a + b + (-a + b) Cos[2 e z])/ (1 + Cos[e z])^2] EllipticF[ I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[(e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] Sec[(e z)/2]^2 Sqrt[1 + (b Tan[(e z)/2]^2)/ (2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ (Sqrt[-((-2 a + 2 Sqrt[a] Sqrt[a - b] + b)/b)] ((a + b + (-a + b) Cos[2 e z]) Sec[(e z)/2]^4)^(3/2)) + (Sqrt[2] (-8 a^3 + a^2 b - a b^2 + 8 b^3) (1 + Cos[e z]) Sqrt[(a + b - a Cos[2 e z] + b Cos[2 e z])/(1 + Cos[e z])^2] (((-(1/2)) (a + b + (-a + b) Cos[2 e z]) Sec[(e z)/2]^2 Tan[(e z)/2] + (I (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) (EllipticE[I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[ (e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] - EllipticF[ I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[ (e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)]) Sqrt[1 + (b Tan[(e z)/2]^2)/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] - (I a EllipticF[I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[(e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] Sqrt[1 + (b Tan[(e z)/2]^2)/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)])/ ((a - b) Sqrt[4 a Tan[(e z)/2]^2 + b (-1 + Tan[(e z)/2]^2)^2])))/ Sqrt[a + b + (-a + b) Cos[2 e z]])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]], "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]], "2"]]]]], ")"]], RowBox[List["5", "/", "2"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[FractionBox["1", "e"], RowBox[List["(", RowBox[List[FractionBox["1", RowBox[List["60", " ", SqrtBox["2"]]]], RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "11"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]], ")"]]]], ")"]]]], "+", RowBox[List[FractionBox["1", RowBox[List["15", " ", SqrtBox["2"], " ", "e"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List["7", " ", SuperscriptBox["a", "2"], " ", "b"]], "+", RowBox[List["7", " ", "a", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], "2"]]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], ")"]]]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], "b"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "4"]]], ")"]], RowBox[List["3", "/", "2"]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "b"]], "-", RowBox[List["a", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", "b", "-", RowBox[List["a", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], "2"]]], " ", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], "-", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]]]], ")"]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["4", " ", "a", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], ")"]], "2"]]]]]]]], ")"]]]]]], ")"]], "/", RowBox[List["(", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], ")"]]]]]], ")"]]]]]]]]]]










MathML Form







<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> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> cos </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> sin </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mn> 15 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mi> e </mi> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 8 </mn> </mrow> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mi> cos </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> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> cos </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> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sec </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <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> <mrow> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> - </mo> <mrow> <mi> F </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> <mrow> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> F </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> <mrow> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> a </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> b </mi> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <mi> b </mi> <mo> &#8290; </mo> <msup> <mi> a </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 2 </mn> </msup> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 8 </mn> <mo> &#8290; </mo> <msup> <mi> b </mi> <mn> 3 </mn> </msup> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> </msqrt> <mo> &#8290; </mo> <msqrt> <mfrac> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mi> cos </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> F </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> <mrow> <msqrt> <mfrac> <mi> b </mi> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> </msqrt> <mo> &#8290; </mo> <mrow> <mi> tan </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#10072; </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msup> <mi> sec </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mi> b </mi> </mrow> </mfrac> <mo> + </mo> <mn> 1 </mn> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mn> 2 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> </mfrac> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> / </mo> <mrow> <mo> ( </mo> <mrow> <msqrt> <mrow> <mo> - </mo> <mfrac> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 2 </mn> </mrow> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> + </mo> <mi> b </mi> </mrow> <mi> b </mi> </mfrac> </mrow> </msqrt> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> sec </mi> <mn> 4 </mn> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <mi> e </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 60 </mn> <mo> &#8290; </mo> <msqrt> <mn> 2 </mn> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 3 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> - </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> <mo> - </mo> <mrow> <mn> 11 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mi> a </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cos </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> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sin </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> <mo> ) </mo> </mrow> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <cos /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <sin /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 15 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> e </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> -8 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <cos /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> <ci> a </ci> </apply> <ci> a </ci> <ci> b </ci> <apply> <times /> <ci> b </ci> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <cos /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </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> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <plus /> <apply> <ci> EllipticE </ci> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> EllipticF </ci> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </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 /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <imaginaryi /> <ci> a </ci> <apply> <ci> EllipticF </ci> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </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> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> a </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <times /> <cn type='integer'> 4 </cn> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <ci> b </ci> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 7 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 3 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <cos /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> EllipticF </ci> <apply> <times /> <imaginaryi /> <apply> <arcsinh /> <apply> <times /> <apply> <power /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <apply> <tan /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </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'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -2 </cn> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <ci> b </ci> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <sec /> <apply> <times /> <ci> e </ci> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <ci> e </ci> <apply> <times /> <cn type='integer'> 60 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 11 </cn> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <cos /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> e </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["a_", " ", SuperscriptBox[RowBox[List["Sin", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]], "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Cos", "[", RowBox[List["e_", " ", "z_"]], "]"]], "2"]]]]], ")"]], RowBox[List["5", "/", "2"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "11"]], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], "+", RowBox[List["3", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], " ", RowBox[List["Sin", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]], RowBox[List["e", " ", RowBox[List["(", RowBox[List["60", " ", SqrtBox["2"]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["8", " ", SuperscriptBox["a", "3"]]], "+", RowBox[List["7", " ", SuperscriptBox["a", "2"], " ", "b"]], "+", RowBox[List["7", " ", "a", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], "2"]]], " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], RowBox[List[SqrtBox[RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], "b"]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "4"]]], ")"]], RowBox[List["3", "/", "2"]]]]]]]], "+", FractionBox[RowBox[List[SqrtBox["2"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "8"]], " ", SuperscriptBox["a", "3"]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "b"]], "-", RowBox[List["a", " ", SuperscriptBox["b", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox["b", "3"]]]]], ")"]], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], " ", SqrtBox[FractionBox[RowBox[List["a", "+", "b", "-", RowBox[List["a", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List["1", "+", RowBox[List["Cos", "[", RowBox[List["e", " ", "z"]], "]"]]]], ")"]], "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], " ", RowBox[List["(", RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Sec", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "+", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["EllipticE", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], "-", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]]]], ")"]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "a", " ", RowBox[List["EllipticF", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", RowBox[List["ArcSinh", "[", RowBox[List[SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]], " ", RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]]]], "]"]]]], ",", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "-", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]], "]"]], " ", SqrtBox[RowBox[List["1", "+", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]], " ", SqrtBox[RowBox[List["1", "-", FractionBox[RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "+", "b"]]]]]]]], SqrtBox[FractionBox["b", RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox["a"], " ", SqrtBox[RowBox[List["a", "-", "b"]]]]], "-", "b"]]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SqrtBox[RowBox[List[RowBox[List["4", " ", "a", " ", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", SuperscriptBox[RowBox[List["Tan", "[", FractionBox[RowBox[List["e", " ", "z"]], "2"], "]"]], "2"]]], ")"]], "2"]]]]]]]], ")"]], " ", SqrtBox[RowBox[List["a", "+", "b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", RowBox[List["Cos", "[", RowBox[List["2", " ", "e", " ", "z"]], "]"]]]]]]]]]]]], RowBox[List["15", " ", SqrtBox["2"], " ", "e"]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2002-12-18