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/01.20.21.1240.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18