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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving rational functions > Involving a z2+b/z2+c





http://functions.wolfram.com/01.19.21.0410.01









  


  










Input Form





Integrate[Sinh[a z^2 + b/z^2 + c], z] == (-(1/8)) E^c Sqrt[Pi] ((1/Sqrt[-a]) ((-1 + Erf[Sqrt[-b]/z - Sqrt[-a] z] - E^(4 Sqrt[-a] Sqrt[-b]) (-1 + Erf[Sqrt[-b]/z + Sqrt[-a] z]))/ E^(2 Sqrt[-a] Sqrt[-b])) + (1/Sqrt[a]) ((1 - Erf[Sqrt[b]/z - Sqrt[a] z] + E^(4 Sqrt[a] Sqrt[b]) (-1 + Erf[Sqrt[b]/z + Sqrt[a] z]))/E^(2 (Sqrt[a] Sqrt[b] + c))))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "2"]]], "+", FractionBox["b_", SuperscriptBox["z_", "2"]], "+", "c_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "8"]]], " ", SuperscriptBox["\[ExponentialE]", "c"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", SqrtBox[RowBox[List["-", "a"]]], " ", SqrtBox[RowBox[List["-", "b"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Erf", "[", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", "b"]]], "z"], "-", RowBox[List[SqrtBox[RowBox[List["-", "a"]]], " ", "z"]]]], "]"]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox[RowBox[List["-", "a"]]], " ", SqrtBox[RowBox[List["-", "b"]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Erf", "[", RowBox[List[FractionBox[SqrtBox[RowBox[List["-", "b"]]], "z"], "+", RowBox[List[SqrtBox[RowBox[List["-", "a"]]], " ", "z"]]]], "]"]]]], ")"]]]]]], ")"]]]], SqrtBox[RowBox[List["-", "a"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SqrtBox["a"], " ", SqrtBox["b"]]], "+", "c"]], ")"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["Erf", "[", RowBox[List[FractionBox[SqrtBox["b"], "z"], "-", RowBox[List[SqrtBox["a"], " ", "z"]]]], "]"]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["4", " ", SqrtBox["a"], " ", SqrtBox["b"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["Erf", "[", RowBox[List[FractionBox[SqrtBox["b"], "z"], "+", RowBox[List[SqrtBox["a"], " ", "z"]]]], "]"]]]], ")"]]]]]], ")"]]]], SqrtBox["a"]]]], ")"]]]]]]]]










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





2002-12-18