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 Cosh

 http://functions.wolfram.com/01.20.21.1331.01

 Input Form

 Integrate[(E^(p z) Cosh[d z])/(a Sin[e z]^2 + b Cos[e z]^2), z] == (1/2) (-((I E^((-d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[1 - (I (-d + p))/(2 e), 1, 2 - (I (-d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[1 - (I (-d + p))/(2 e), 1, 2 - (I (-d + p))/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] + I Sqrt[b])^2]))/(Sqrt[-a] Sqrt[b] (-a + b) (-d + 2 I e + p))) - (I E^((d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[1 - (I (d + p))/(2 e), 1, 2 - (I (d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^ 2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[ 1 - (I (d + p))/(2 e), 1, 2 - (I (d + p))/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^2]))/ (Sqrt[-a] Sqrt[b] (-a + b) (d + 2 I e + p)))

 Standard Form

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 MathML Form

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

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

 2002-12-18