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 Cos

 http://functions.wolfram.com/01.07.21.2676.01

 Input Form

 Integrate[(E^(p z) Sin[d z])/(a Sin[e z]^2 + b Cos[e z]^2), z] == ((1/((-I) d + 2 I e + p)) (E^(((-I) d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[1 - (d + I p)/(2 e), 1, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^ 2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[ 1 - (d + I p)/(2 e), 1, 2 - (d + I p)/(2 e), ((-a + b) E^(2 I e z))/ (Sqrt[-a] + I Sqrt[b])^2])) - (1/(I d + 2 I e + p)) (E^((I d + 2 I e + p) z) ((Sqrt[-a] + I Sqrt[b])^2 Hypergeometric2F1[(d + 2 e - I p)/(2 e), 1, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] - I Sqrt[b])^2] - (Sqrt[-a] - I Sqrt[b])^2 Hypergeometric2F1[(d + 2 e - I p)/(2 e), 1, (d + 4 e - I p)/(2 e), ((-a + b) E^(2 I e z))/(Sqrt[-a] + I Sqrt[b])^ 2])))/(2 Sqrt[-a] Sqrt[b] (-a + b))

 Standard Form

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 MathML Form

 p z sin ( d z ) a sin 2 ( e z ) + b cos 2 ( e z ) z 1 2 - a b ( b - a ) ( 1 - 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["d", "+", 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["d", "+", RowBox[List["\[ImaginaryI]", " ", "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 ; 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["d", "+", 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["d", "+", RowBox[List["\[ImaginaryI]", " ", "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] ) ) - 1 d + 2 e + p ( ( d + 2 e + p ) z ( ( - a + b ) 2 2 F 1 ( d + 2 e - p 2 e , 1 ; d + 4 e - 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[FractionBox[RowBox[List["d", "+", RowBox[List["2", " ", "e"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "e"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "+", RowBox[List["4", " ", "e"]], "-", RowBox[List["\[ImaginaryI]", " ", "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 ( d + 2 e - p 2 e , 1 ; d + 4 e - 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[FractionBox[RowBox[List["d", "+", RowBox[List["2", " ", "e"]], "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "e"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List["d", "+", RowBox[List["4", " ", "e"]], "-", RowBox[List["\[ImaginaryI]", " ", "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] ) ) ) z p z d z a e z 2 b e z 2 -1 1 2 -1 a 1 2 b 1 2 b -1 a -1 1 -1 d 2 e p -1 -1 d 2 e p z -1 a 1 2 b 1 2 2 Hypergeometric2F1 1 -1 d p 2 e -1 1 2 -1 d p 2 e -1 b -1 a 2 e z -1 a 1 2 -1 b 1 2 2 -1 -1 -1 a 1 2 -1 b 1 2 2 Hypergeometric2F1 1 -1 d p 2 e -1 1 2 -1 d p 2 e -1 b -1 a 2 e z -1 a 1 2 b 1 2 2 -1 -1 1 d 2 e p -1 d 2 e p z -1 a 1 2 b 1 2 2 Hypergeometric2F1 d 2 e -1 p 2 e -1 1 d 4 e -1 p 2 e -1 b -1 a 2 e z -1 a 1 2 -1 b 1 2 2 -1 -1 -1 a 1 2 -1 b 1 2 2 Hypergeometric2F1 d 2 e -1 p 2 e -1 1 d 4 e -1 p 2 e -1 b -1 a 2 e z -1 a 1 2 b 1 2 2 -1 [/itex]

 Rule Form

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

 2002-12-18