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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving rational functions > Involving (a z+b)-n





http://functions.wolfram.com/01.19.21.0143.01









  


  










Input Form





Integrate[(z^2 Sinh[c z])/(a z + b), z] == (1/(a^3 c^2)) ((-b^2) c^2 CoshIntegral[c (b/a + z)] Sinh[(b c)/a] + a ((-c) (b - a z) Cosh[c z] - a Sinh[c z]) + b^2 c^2 Cosh[(b c)/a] SinhIntegral[c (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[SuperscriptBox["z_", "2"], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List[RowBox[List["a_", " ", "z_"]], "+", "b_"]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["b", "2"]]], " ", SuperscriptBox["c", "2"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]], "]"]], " ", RowBox[List["Sinh", "[", FractionBox[RowBox[List["b", " ", "c"]], "a"], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["(", RowBox[List["b", "-", RowBox[List["a", " ", "z"]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "-", RowBox[List["a", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["c", "2"], " ", RowBox[List["Cosh", "[", FractionBox[RowBox[List["b", " ", "c"]], "a"], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["c", " ", RowBox[List["(", RowBox[List[FractionBox["b", "a"], "+", "z"]], ")"]]]], "]"]]]]]], RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["c", "2"]]]]]]]]










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





2002-12-18