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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function > Involving power > Involving zalpha-1and arguments a z+b





http://functions.wolfram.com/01.19.21.0082.01









  


  










Input Form





Integrate[(1/z^(9/2)) Sinh[b + a z], z] == (-(1/(105 z^(7/2)))) (2 (6 a z Cosh[b + a z] + 8 a^3 z^3 Cosh[b + a z] + 4 a^(7/2) Sqrt[Pi] z^(7/2) Erf[Sqrt[a] Sqrt[z]] (Cosh[b] - Sinh[b]) - 4 a^(7/2) Sqrt[Pi] z^(7/2) Erfi[Sqrt[a] Sqrt[z]] (Cosh[b] + Sinh[b]) + 15 Sinh[b + a z] + 4 a^2 z^2 Sinh[b + a z]))










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[FractionBox[RowBox[List["Sinh", "[", RowBox[List["b_", "+", RowBox[List["a_", " ", "z_"]]]], "]"]], SuperscriptBox["z_", RowBox[List["9", "/", "2"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["8", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["a", RowBox[List["7", "/", "2"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erf", "[", RowBox[List[SqrtBox["a"], " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "b", "]"]], "-", RowBox[List["Sinh", "[", "b", "]"]]]], ")"]]]], "-", RowBox[List["4", " ", SuperscriptBox["a", RowBox[List["7", "/", "2"]]], " ", SqrtBox["\[Pi]"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erfi", "[", RowBox[List[SqrtBox["a"], " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "b", "]"]], "+", RowBox[List["Sinh", "[", "b", "]"]]]], ")"]]]], "+", RowBox[List["15", " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]], "+", RowBox[List["4", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", "z"]]]], "]"]]]]]], ")"]]]], RowBox[List["105", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]]]










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





2002-12-18