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/01.20.21.0869.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18