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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1 eb z sinh(c z)





http://functions.wolfram.com/01.19.21.0284.01









  


  










Input Form





Integrate[z^2 E^(b z) Sinh[c z], z] == (1/((c - b)^3 (c + b)^3)) (E^(b z) (c (c^4 z^2 + c^2 (2 + 4 b z - 2 b^2 z^2) + b^2 (6 - 4 b z + b^2 z^2)) Cosh[c z] - (c^4 z (2 + b z) + b^3 (2 - 2 b z + b^2 z^2) + c^2 (6 b - 2 b^3 z^2)) Sinh[c 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[RowBox[List[SuperscriptBox["z_", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["c", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["c", "4"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["4", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["6", "-", RowBox[List["4", " ", "b", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["c", "4"], " ", "z", " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["b", " ", "z"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "3"], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["c", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["6", " ", "b"]], "-", RowBox[List["2", " ", SuperscriptBox["b", "3"], " ", SuperscriptBox["z", "2"]]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], "3"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]], "3"]]]]]]]]










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





2002-12-18