html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cos

 http://functions.wolfram.com/01.07.21.2687.01

 Input Form

 Integrate[E^(p z)/(a Sin[e z]^2 + b Sin[2 e z] + c Cos[e z]^2)^2, z] == (((-I) a + 2 b + I c) E^((2 I e + p) z) ((-(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]))] - (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])] + 2 ((-2 b^2 + c Sqrt[-b^2 + a c] + a (2 c + Sqrt[-b^2 + a c])) Hypergeometric2F1[1 - (I p)/(2 e), 2, 2 - (I p)/(2 e), -(((-a - 2 I b + c) E^(2 I e z))/(a + c - 2 Sqrt[-b^2 + a c]))] + (2 b^2 + c Sqrt[-b^2 + a c] + a (-2 c + Sqrt[-b^2 + a c])) Hypergeometric2F1[1 - (I p)/(2 e), 2, 2 - (I p)/(2 e), ((a + 2 I b - c) E^(2 I e z))/(a + c + 2 Sqrt[-b^2 + a c])])))/ (2 (-b^2 + a c)^(3/2) (a + c - 2 Sqrt[-b^2 + a c]) (a + c + 2 Sqrt[-b^2 + a c]) (2 e - I 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 ) ) 2 z ( ( 2 b - a + c ) ( 2 e + p ) z ( - ( a + c ) ( - 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 ) ( a + c + 2 a c - b 2 ) 2 F 1 ( 1 - p 2 e , 1 ; 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 Rule Form

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

 2002-12-18