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 Cosh

 http://functions.wolfram.com/01.20.21.4247.01

 Input Form

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

 Standard Form

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 MathML Form

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

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

 2002-12-18