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 Cosh

 http://functions.wolfram.com/01.20.21.1328.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18