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; }

 Cosh

 http://functions.wolfram.com/01.20.21.1334.01

 Input Form

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

 Standard Form

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 MathML Form

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

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

 2002-12-18