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 Cos

 http://functions.wolfram.com/01.07.21.2686.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18