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 Cosh

 http://functions.wolfram.com/01.20.21.4720.01

 Input Form

 Integrate[E^(p z)/(a Sinh[e z]^2 + b Sinh[2 e z] + c Cosh[e z]^2)^2, z] == ((a + 2 b + c) E^((2 e + p) z) ((a - c) (a - c + 2 Sqrt[b^2 - a c]) Hypergeometric2F1[1 + p/(2 e), 1, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/ (a - c - 2 Sqrt[b^2 - a c])] + (a - c) (-a + c + 2 Sqrt[b^2 - a c]) Hypergeometric2F1[1 + p/(2 e), 1, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/ (a - c + 2 Sqrt[b^2 - a c])] - 4 b^2 Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c - 2 Sqrt[b^2 - a c])] + 4 a c Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c - 2 Sqrt[b^2 - a c])] - 2 a Sqrt[b^2 - a c] Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c - 2 Sqrt[b^2 - a c])] + 2 c Sqrt[b^2 - a c] Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c - 2 Sqrt[b^2 - a c])] + 4 b^2 Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c + 2 Sqrt[b^2 - a c])] - 4 a c Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c + 2 Sqrt[b^2 - a c])] - 2 a Sqrt[b^2 - a c] Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c + 2 Sqrt[b^2 - a c])] + 2 c Sqrt[b^2 - a c] Hypergeometric2F1[1 + p/(2 e), 2, 2 + p/(2 e), ((a + 2 b + c) E^(2 e z))/(a - c + 2 Sqrt[b^2 - a c])]))/ (2 (b^2 - a c)^(3/2) (a - c + 2 Sqrt[b^2 - a c]) (-a + c + 2 Sqrt[b^2 - a c]) (2 e + p))

 Standard Form

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 MathML Form

 p z ( a sinh 2 ( e z ) + b sinh ( 2 e z ) + c cosh 2 ( e z ) ) 2 z ( ( a + 2 b + c ) ( 2 e + p ) z ( 4 2 F 1 ( p 2 e + 1 , 2 ; p 2 e + 2 ; ( a + 2 b + c ) 2 e z a - c + 2 b 2 - a c ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["p", RowBox[List["2", " ", "e"]]], "+", "1"]], Hypergeometric2F1], ",", TagBox["2", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List[FractionBox["p", RowBox[List["2", " ", "e"]]], "+", "2"]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", RowBox[List["2", " ", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "e", " ", "z"]]]]], RowBox[List["a", "-", "c", "+", RowBox[List["2", " ", SqrtBox[RowBox[List[SuperscriptBox["b", "2"], "-", RowBox[List["a", " ", "c"]]]]]]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] b 2 - 4 2 F 1 ( p 2 e + 1 , 2 ; 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 Rule Form

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

 2002-12-18