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 Cosh

 http://functions.wolfram.com/01.20.21.1327.01

 Input Form

 Integrate[(E^(p z) Cosh[d z])/(a Sin[e z] + b Cos[e z]), z] == (1/(I a + b)) (-((1/(d - I e - p)) (E^((-d + I e + p) z) Hypergeometric2F1[(I d + e - I p)/(2 e), 1, (I (d - 3 I e - p))/(2 e), ((a + I b) E^(2 I e z))/(a - I b)])) + (1/(d + I e + p)) (E^((d + I e + p) z) Hypergeometric2F1[ -((I (d + I e + p))/(2 e)), 1, -((I (d + 3 I e + 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 ) z 1 b + a ( ( d + e + p ) z d + e + p 2 F 1 ( - ( d + e + p ) 2 e , 1 ; - ( d + 3 e + 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["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["\[ImaginaryI]", " ", "e"]], " ", "+", "p"]], ")"]]]], RowBox[List["2", " ", "e"]]]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "+", RowBox[List["3", " ", "\[ImaginaryI]", " ", "e"]], " ", "+", "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 + e + p ) z d - e - p 2 F 1 ( e + d - p 2 e , 1 ; ( d - 3 e - 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[FractionBox[RowBox[List["e", "+", RowBox[List["\[ImaginaryI]", " ", "d"]], " ", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "e"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["d", "-", RowBox[List["3", " ", "\[ImaginaryI]", " ", "e"]], "-", "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] ) z p z d z a e z b e z -1 1 b a -1 d e p z d e p -1 Hypergeometric2F1 -1 d e p 2 e -1 1 -1 d 3 e p 2 e -1 a b 2 e z a -1 b -1 -1 -1 d e p z d -1 e -1 p -1 Hypergeometric2F1 e d -1 p 2 e -1 1 d -1 3 e -1 p 2 e -1 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