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 Cosh

 http://functions.wolfram.com/01.20.21.4262.01

 Input Form

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

 Standard Form

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 MathML Form

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

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

 2002-12-18