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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 zr+b





http://functions.wolfram.com/01.19.21.0134.01









  


  










Input Form





Integrate[(1/z^4) Sinh[a Sqrt[z] + b], z] == (-(1/(360 z^3))) (24 a Sqrt[z] Cosh[b + a Sqrt[z]] + 2 a^3 z^(3/2) Cosh[b + a Sqrt[z]] + a^5 z^(5/2) Cosh[b + a Sqrt[z]] - a^6 z^3 CoshIntegral[a Sqrt[z]] Sinh[b] + 120 Sinh[b + a Sqrt[z]] + 6 a^2 z Sinh[b + a Sqrt[z]] + a^4 z^2 Sinh[b + a Sqrt[z]] - a^6 z^3 Cosh[b] SinhIntegral[a Sqrt[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[RowBox[List["a_", " ", SqrtBox["z_"]]], "+", "b_"]], "]"]], SuperscriptBox["z_", "4"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["24", " ", "a", " ", SqrtBox["z"], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["2", " ", SuperscriptBox["a", "3"], " ", SuperscriptBox["z", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "5"], " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]], " ", RowBox[List["Cosh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Sinh", "[", "b", "]"]]]], "+", RowBox[List["120", " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List["6", " ", SuperscriptBox["a", "2"], " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["Sinh", "[", RowBox[List["b", "+", RowBox[List["a", " ", SqrtBox["z"]]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["a", "6"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["Cosh", "[", "b", "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", SqrtBox["z"]]], "]"]]]]]], RowBox[List["360", " ", SuperscriptBox["z", "3"]]]]]]]]]]










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





2002-12-18