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 Cos

 http://functions.wolfram.com/01.07.21.2668.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18