html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4282.01

 Input Form

 Integrate[(A + B Sinh[z] + C Cosh[z])/((a + b Sinh[z] + c Cosh[z]) (\[Alpha] + \[Beta] Sinh[z] + \[Gamma] Cosh[z])), z] == (2 (((-a) b B + A (b^2 - c^2) + a c C) \[Alpha] + ((-a) A b + a^2 B - B c^2 + b c C) \[Beta] + (a A c + b B c - a^2 C - b^2 C) \[Gamma]) ArcTan[(b + (-a + c) Tanh[z/2])/Sqrt[-a^2 - b^2 + c^2]])/ (Sqrt[-a^2 - b^2 + c^2] ((b^2 - c^2) \[Alpha]^2 + (a^2 - c^2) \[Beta]^2 + 2 b c \[Beta] \[Gamma] - (a^2 + b^2) \[Gamma]^2 + \[Alpha] (-2 a b \[Beta] + 2 a c \[Gamma]))) + (2 ((b B - c C) \[Alpha]^2 + (a A - c C) \[Beta]^2 + (B c + b C) \[Beta] \[Gamma] - (a A + b B) \[Gamma]^2 + \[Alpha] (((-A) b - a B) \[Beta] + (A c + a C) \[Gamma])) ArcTan[(\[Beta] + (-\[Alpha] + \[Gamma]) Tanh[z/2])/ Sqrt[-\[Alpha]^2 - \[Beta]^2 + \[Gamma]^2]])/ (Sqrt[-\[Alpha]^2 - \[Beta]^2 + \[Gamma]^2] ((b^2 - c^2) \[Alpha]^2 + (a^2 - c^2) \[Beta]^2 + 2 b c \[Beta] \[Gamma] - (a^2 + b^2) \[Gamma]^2 + \[Alpha] (-2 a b \[Beta] + 2 a c \[Gamma]))) + (((B c - b C) \[Alpha] + ((-A) c + a C) \[Beta] + (A b - a B) \[Gamma]) Log[a + c Cosh[z] + b Sinh[z]])/((-b^2 + c^2) \[Alpha]^2 + (-a^2 + c^2) \[Beta]^2 - 2 b c \[Beta] \[Gamma] + (a^2 + b^2) \[Gamma]^2 + 2 a \[Alpha] (b \[Beta] - c \[Gamma])) - (((B c - b C) \[Alpha] + ((-A) c + a C) \[Beta] + (A b - a B) \[Gamma]) Log[\[Alpha] + \[Gamma] Cosh[z] + \[Beta] Sinh[z]])/ ((-b^2 + c^2) \[Alpha]^2 + (-a^2 + c^2) \[Beta]^2 - 2 b c \[Beta] \[Gamma] + (a^2 + b^2) \[Gamma]^2 + 2 a \[Alpha] (b \[Beta] - c \[Gamma]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["A", "+", RowBox[List["B", " ", RowBox[List["Sinh", "[", "z", "]"]]]], "+", RowBox[List["C", " ", RowBox[List["Cosh", "[", "z", "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", "z", "]"]]]], "+", RowBox[List["c", " ", RowBox[List["Cosh", "[", "z", "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Alpha]", "+", RowBox[List["\[Beta]", " ", RowBox[List["Sinh", "[", "z", "]"]]]], "+", RowBox[List["\[Gamma]", " ", RowBox[List["Cosh", "[", "z", "]"]]]]]], ")"]]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", "B"]], "+", RowBox[List["A", " ", RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]]]], "+", RowBox[List["a", " ", "c", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "A", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "B"]], "-", RowBox[List["B", " ", SuperscriptBox["c", "2"]]], "+", RowBox[List["b", " ", "c", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A", " ", "c"]], "+", RowBox[List["b", " ", "B", " ", "c"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "C"]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", "C"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "c"]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "b", " ", "\[Beta]"]], "+", RowBox[List["2", " ", "a", " ", "c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", "B"]], "-", RowBox[List["c", " ", "C"]]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A"]], "-", RowBox[List["c", " ", "C"]]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "+", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A"]], "+", RowBox[List["b", " ", "B"]]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["\[Beta]", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[Alpha]"]], "+", "\[Gamma]"]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["\[Alpha]", "2"]]], "-", SuperscriptBox["\[Beta]", "2"], "+", SuperscriptBox["\[Gamma]", "2"]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["\[Alpha]", "2"]]], "-", SuperscriptBox["\[Beta]", "2"], "+", SuperscriptBox["\[Gamma]", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "b", " ", "\[Beta]"]], "+", RowBox[List["2", " ", "a", " ", "c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "-", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["c", " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "-", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["2", " ", "a", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Beta]"]], "-", RowBox[List["c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "-", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["\[Alpha]", "+", RowBox[List["\[Gamma]", " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["\[Beta]", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "-", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["2", " ", "a", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Beta]"]], "-", RowBox[List["c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]]]]]]]]

 MathML Form

 A + C cosh ( z ) + B sinh ( z ) ( a + c cosh ( z ) + b sinh ( z ) ) ( α + β Sinh ( z ) + γ Cosh ( z ) ) z ( 2 ( ( - a b B + A ( b 2 - c 2 ) + a c C ) α + ( B a 2 - B c 2 - a A b + b c C ) β + ( - C a 2 + A c a + b B c - b 2 C ) γ ) tan - 1 ( b + ( c - a ) tanh ( z 2 ) - a 2 - b 2 + c 2 ) ) / ( - a 2 - b 2 + c 2 ( ( b 2 - c 2 ) α 2 + ( 2 a c γ - 2 a b β ) α + ( a 2 - c 2 ) β 2 - ( a 2 + b 2 ) γ 2 + 2 b c β γ ) ) + ( 2 ( ( b B - c C ) α 2 + ( ( - A b - a B ) β + ( A c + a C ) γ ) α + ( a A - c C ) β 2 - ( a A + b B ) γ 2 + ( B c + b C ) β γ ) tan - 1 ( β + ( γ - α ) tanh ( z 2 ) - α 2 - β 2 + γ 2 ) ) / ( - α 2 - β 2 + γ 2 ( ( b 2 - c 2 ) α 2 + ( 2 a c γ - 2 a b β ) α + ( a 2 - c 2 ) β 2 - ( a 2 + b 2 ) γ 2 + 2 b c β γ ) ) + ( ( B c - b C ) α + ( a C - A c ) β + ( A b - a B ) γ ) log ( a + c cosh ( z ) + b sinh ( z ) ) ( c 2 - b 2 ) α 2 + 2 a ( b β - c γ ) α + ( c 2 - a 2 ) β 2 + ( a 2 + b 2 ) γ 2 - 2 b c β γ - ( ( B c - b C ) α + ( a C - A c ) β + ( A b - a B ) γ ) log ( α + γ cosh ( z ) + β sinh ( z ) ) ( c 2 - b 2 ) α 2 + 2 a ( b β - c γ ) α + ( c 2 - a 2 ) β 2 + ( a 2 + b 2 ) γ 2 - 2 b c β γ z A C z B z a c z b z α β z γ z -1 2 -1 a b B A b 2 -1 c 2 a c C α B a 2 -1 B c 2 -1 a A b b c C β -1 C a 2 A c a b B c -1 b 2 C γ b c -1 a z 2 -1 -1 a 2 -1 b 2 c 2 1 2 -1 -1 a 2 -1 b 2 c 2 1 2 b 2 -1 c 2 α 2 2 a c γ -1 2 a b β α a 2 -1 c 2 β 2 -1 a 2 b 2 γ 2 2 b c β γ -1 2 b B -1 c C α 2 -1 A b -1 a B β A c a C γ α a A -1 c C β 2 -1 a A b B γ 2 B c b C β γ β γ -1 α z 2 -1 -1 α 2 -1 β 2 γ 2 1 2 -1 -1 α 2 -1 β 2 γ 2 1 2 b 2 -1 c 2 α 2 2 a c γ -1 2 a b β α a 2 -1 c 2 β 2 -1 a 2 b 2 γ 2 2 b c β γ -1 B c -1 b C α a C -1 A c β A b -1 a B γ a c z b z c 2 -1 b 2 α 2 2 a b β -1 c γ α c 2 -1 a 2 β 2 a 2 b 2 γ 2 -1 2 b c β γ -1 -1 B c -1 b C α a C -1 A c β A b -1 a B γ α γ z β z c 2 -1 b 2 α 2 2 a b β -1 c γ α c 2 -1 a 2 β 2 a 2 b 2 γ 2 -1 2 b c β γ -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List["A_", "+", RowBox[List["B_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]], "+", RowBox[List["C", " ", RowBox[List["Cosh", "[", "z_", "]"]]]]]], RowBox[List[RowBox[List["(", RowBox[List["a_", "+", RowBox[List["b_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]], "+", RowBox[List["c_", " ", RowBox[List["Cosh", "[", "z_", "]"]]]]]], ")"]], " ", RowBox[List["(", RowBox[List["\[Alpha]_", "+", RowBox[List["\[Beta]_", " ", RowBox[List["Sinh", "[", "z_", "]"]]]], "+", RowBox[List["\[Gamma]_", " ", RowBox[List["Cosh", "[", "z_", "]"]]]]]], ")"]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", "B"]], "+", RowBox[List["A", " ", RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]]]], "+", RowBox[List["a", " ", "c", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "A", " ", "b"]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", "B"]], "-", RowBox[List["B", " ", SuperscriptBox["c", "2"]]], "+", RowBox[List["b", " ", "c", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A", " ", "c"]], "+", RowBox[List["b", " ", "B", " ", "c"]], "-", RowBox[List[SuperscriptBox["a", "2"], " ", "C"]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", "C"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["b", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "c"]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]]], "]"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "-", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "b", " ", "\[Beta]"]], "+", RowBox[List["2", " ", "a", " ", "c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["b", " ", "B"]], "-", RowBox[List["c", " ", "C"]]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A"]], "-", RowBox[List["c", " ", "C"]]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "+", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["a", " ", "A"]], "+", RowBox[List["b", " ", "B"]]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]]]]]], ")"]], " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["\[Beta]", "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "\[Alpha]"]], "+", "\[Gamma]"]], ")"]], " ", RowBox[List["Tanh", "[", FractionBox["z", "2"], "]"]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["\[Alpha]", "2"]]], "-", SuperscriptBox["\[Beta]", "2"], "+", SuperscriptBox["\[Gamma]", "2"]]]]], "]"]]]], RowBox[List[SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox["\[Alpha]", "2"]]], "-", SuperscriptBox["\[Beta]", "2"], "+", SuperscriptBox["\[Gamma]", "2"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "+", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "a", " ", "b", " ", "\[Beta]"]], "+", RowBox[List["2", " ", "a", " ", "c", " ", "\[Gamma]"]]]], ")"]]]]]], ")"]]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "-", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["a", "+", RowBox[List["c", " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "-", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["2", " ", "a", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Beta]"]], "-", RowBox[List["c", " ", "\[Gamma]"]]]], ")"]]]]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["B", " ", "c"]], "-", RowBox[List["b", " ", "C"]]]], ")"]], " ", "\[Alpha]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "A"]], " ", "c"]], "+", RowBox[List["a", " ", "C"]]]], ")"]], " ", "\[Beta]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["A", " ", "b"]], "-", RowBox[List["a", " ", "B"]]]], ")"]], " ", "\[Gamma]"]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List["\[Alpha]", "+", RowBox[List["\[Gamma]", " ", RowBox[List["Cosh", "[", "z", "]"]]]], "+", RowBox[List["\[Beta]", " ", RowBox[List["Sinh", "[", "z", "]"]]]]]], "]"]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Alpha]", "2"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["a", "2"]]], "+", SuperscriptBox["c", "2"]]], ")"]], " ", SuperscriptBox["\[Beta]", "2"]]], "-", RowBox[List["2", " ", "b", " ", "c", " ", "\[Beta]", " ", "\[Gamma]"]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", SuperscriptBox["\[Gamma]", "2"]]], "+", RowBox[List["2", " ", "a", " ", "\[Alpha]", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "\[Beta]"]], "-", RowBox[List["c", " ", "\[Gamma]"]]]], ")"]]]]]]]]]]]]]

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

 2002-12-18