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 Cos

 http://functions.wolfram.com/01.07.21.2655.01

 Input Form

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

 Standard Form

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 MathML Form

 p z sin ( d z ) a + b cos 2 ( c z ) z 2 a b a + b ( 1 2 c + d + p ( ( 2 c + d + p ) z ( ( 2 a - 2 a + b a + b ) 2 F 1 ( 2 c + d - p 2 c , 1 ; 4 c + d - p 2 c ; - b 2 c z 2 a + 2 a + b 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[RowBox[List["2", " ", "c"]], "+", "d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "c"]], "+", "d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", SqrtBox["a"]]], "+", "b"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - ( 2 a + 2 a + b a + b ) 2 F 1 ( 2 c + d - p 2 c , 1 ; 4 c + d - p 2 c ; - b 2 c z 2 a - 2 a + b 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[RowBox[List["2", " ", "c"]], "+", "d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], ",", TagBox["1", Hypergeometric2F1]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[TagBox[TagBox[FractionBox[RowBox[List[RowBox[List["4", " ", "c"]], "+", "d", "-", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", SqrtBox["a"]]], "+", "b"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) - 1 2 c - d + p ( ( 2 c - d + p ) z ( ( 2 a - 2 a + b a + b ) 2 F 1 ( 1 - d + p 2 c , 1 ; 2 - d + p 2 c ; - b 2 c z 2 a + 2 a + b 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["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]]]], 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", " ", "c"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "+", RowBox[List["2", " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", SqrtBox["a"]]], "+", "b"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] - ( 2 a + 2 a + b a + b ) 2 F 1 ( 1 - d + p 2 c , 1 ; 2 - d + p 2 c ; - b 2 c z 2 a - 2 a + b 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["d", "+", RowBox[List["\[ImaginaryI]", " ", "p"]]]], RowBox[List["2", " ", "c"]]]]], 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", " ", "c"]]]]], Hypergeometric2F1], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1], ";", TagBox[RowBox[List["-", FractionBox[RowBox[List["b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", "c", " ", "z"]]]]], RowBox[List[RowBox[List["2", " ", "a"]], "-", RowBox[List["2", " ", SqrtBox[RowBox[List["a", "+", "b"]]], " ", SqrtBox["a"]]], "+", "b"]]]]], Hypergeometric2F1]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]]], Hypergeometric2F1] ) ) ) z p z d z a b c z 2 -1 2 a 1 2 b a b 1 2 -1 1 2 c d p -1 2 c d p z 2 a -1 2 a b 1 2 a 1 2 b Hypergeometric2F1 2 c d -1 p 2 c -1 1 4 c d -1 p 2 c -1 -1 b 2 c z 2 a 2 a b 1 2 a 1 2 b -1 -1 2 a 2 a b 1 2 a 1 2 b Hypergeometric2F1 2 c d -1 p 2 c -1 1 4 c d -1 p 2 c -1 -1 b 2 c z 2 a -1 2 a b 1 2 a 1 2 b -1 -1 1 2 c -1 d p -1 2 c -1 d p z 2 a -1 2 a b 1 2 a 1 2 b Hypergeometric2F1 1 -1 d p 2 c -1 1 2 -1 d p 2 c -1 -1 b 2 c z 2 a 2 a b 1 2 a 1 2 b -1 -1 2 a 2 a b 1 2 a 1 2 b Hypergeometric2F1 1 -1 d p 2 c -1 1 2 -1 d p 2 c -1 -1 b 2 c z 2 a -1 2 a b 1 2 a 1 2 b -1 [/itex]

 Rule Form

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

 2002-12-18