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 Cos

 http://functions.wolfram.com/01.07.21.2696.01

 Input Form

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

 Standard Form

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 MathML Form

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