Integrate[1/(a Sinh[z] + b Sech[z]), z] == ((1/4 + I/4) (4 I Sqrt[I a + 2 b] Sqrt[-2 I a + 4 b] ArcTan[((-1 + I) Sqrt[a] + ((1 + I) Sqrt[a] - Sqrt[2 I a + 4 b]) Tanh[z/2])/Sqrt[2 I a - 4 b]] + 2 I Sqrt[I a + 2 b] Sqrt[-2 I a + 4 b] ArcTan[((1 - I) Sqrt[a] - ((1 + I) Sqrt[a] + Sqrt[2 I a + 4 b]) Tanh[z/2])/Sqrt[2 I a - 4 b]] + 4 I Sqrt[I a + 2 b] Sqrt[-2 I a + 4 b] ArcTan[((-1 + I) Sqrt[a] + ((1 + I) Sqrt[a] + Sqrt[2 I a + 4 b]) Tanh[z/2])/Sqrt[2 I a - 4 b]] + 2 I Sqrt[2 I a - 4 b] Sqrt[I a + 2 b] ArcTanh[((-1 + I) Sqrt[a] + ((1 + I) Sqrt[a] - Sqrt[2 I a + 4 b]) Tanh[z/2])/ Sqrt[-2 I a + 4 b]] - Sqrt[2] Sqrt[(a + 2 I b)^2] Log[I (Sqrt[2 I a + 4 b] + (1 + I) Sqrt[a] Cosh[z] - (1 - I) Sqrt[a] Sinh[z])] + Sqrt[2] Sqrt[(a + 2 I b)^2] Log[Sqrt[2 I a + 4 b] - (1 + I) Sqrt[a] Cosh[z] + (1 - I) Sqrt[a] Sinh[z]]))/(Sqrt[a] Sqrt[(a + 2 I b)^2] Sqrt[I a + 2 b])

Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["a", " ", RowBox[List["Sinh", "[", "z", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sech", "[", "z", "]"]]]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[ImaginaryI]", "4"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], ")"]]]], "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]]]], ")"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox["a"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]]]], ")"]]]]]]]]

<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> <mn> 1 </mn> <mrow> <mrow> <mi> b </mi> <mo> &#8290; </mo> <mrow> <mi> sech </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mi> a </mi> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> &#8518; </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <msqrt> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 4 </mn> </mfrac> <mo> + </mo> <mfrac> <mi> &#8520; </mi> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <msqrt> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> <mo> - </mo> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> </msqrt> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <msup> <mi> tanh </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> </mrow> <mo> - </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> tanh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> </mrow> </mrow> </msqrt> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msqrt> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> - </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> &#8290; </mo> <msqrt> <msup> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> b </mi> </mrow> </mrow> <mtext> </mtext> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </msqrt> <mo> &#8290; </mo> <mrow> <mi> log </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> &#8520; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> cosh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#8520; </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msqrt> <mi> a </mi> </msqrt> <mo> &#8290; </mo> <mrow> <mi> sinh </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <msqrt> <mrow> <mrow> <mn> 4 </mn> <mo> &#8290; </mo> <mi> b </mi> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#8520; </mi> <mo> &#8290; </mo> <mi> a </mi> <mtext> </mtext> </mrow> </mrow> </msqrt> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <ci> b </ci> <apply> <sech /> <ci> z </ci> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <arctan /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <tanh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <arctan /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <tanh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <arctan /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <tanh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> </apply> <apply> <times /> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <imaginaryi /> <apply> <arctanh /> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> -1 </cn> <imaginaryi /> </apply> </apply> <apply> <times /> <apply> <plus /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <tanh /> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <sinh /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ln /> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> <apply> <cosh /> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <sinh /> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> b </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> a </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List[RowBox[List["a_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]], "+", RowBox[List["b_", " ", RowBox[List["Sech", "[", "z_", "]"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[ImaginaryI]", "4"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "-", RowBox[List["4", " ", "b"]]]]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]], " ", RowBox[List["ArcTanh", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"]]], "-", SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]]], "]"]]]], "-", RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", RowBox[List["Log", "[", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], ")"]]]], "]"]]]], "+", RowBox[List[SqrtBox["2"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", RowBox[List["Log", "[", RowBox[List[SqrtBox[RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "a"]], "+", RowBox[List["4", " ", "b"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["1", "-", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["a"], " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]]]], ")"]]]], RowBox[List[SqrtBox["a"], " ", SqrtBox[SuperscriptBox[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", "b"]]]], ")"]], "2"]], " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", RowBox[List["2", " ", "b"]]]]]]]]]]]]

2002-12-18