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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving algebraic functions of the direct function > Involving (a+b sinh2(c z))beta sinhnu(c z)





http://functions.wolfram.com/01.19.21.1808.01









  


  










Input Form





Integrate[Sinh[c z]^7/Sqrt[a + b Sinh[c z]^2], z] == (1/(96 b^(7/2) c)) (Sqrt[b] Cosh[c z] Sqrt[4 a - 2 b + 2 b Cosh[2 c z]] (15 a^2 + 19 a b + 23 b^2 - b (5 a + 9 b) Cosh[2 c z] + b^2 Cosh[4 c z]) - 6 (a + b) (5 a^2 - 2 a b + 5 b^2) Log[Sqrt[2] Sqrt[b] Cosh[c z] + Sqrt[2 a - b + b Cosh[2 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[FractionBox[SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "7"], SqrtBox[RowBox[List["a_", "+", RowBox[List["b_", " ", SuperscriptBox[RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]], "2"]]]]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], " ", SqrtBox[RowBox[List[RowBox[List["4", " ", "a"]], "-", RowBox[List["2", " ", "b"]], "+", RowBox[List["2", " ", "b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", SuperscriptBox["a", "2"]]], "+", RowBox[List["19", " ", "a", " ", "b"]], "+", RowBox[List["23", " ", SuperscriptBox["b", "2"]]], "-", RowBox[List["b", " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", "a"]], "+", RowBox[List["9", " ", "b"]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["Cosh", "[", RowBox[List["4", " ", "c", " ", "z"]], "]"]]]]]], ")"]]]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List["5", " ", SuperscriptBox["a", "2"]]], "-", RowBox[List["2", " ", "a", " ", "b"]], "+", RowBox[List["5", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Log", "[", RowBox[List[RowBox[List[SqrtBox["2"], " ", SqrtBox["b"], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", SqrtBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b", "+", RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["2", " ", "c", " ", "z"]], "]"]]]]]]]]], "]"]]]]]], RowBox[List["96", " ", SuperscriptBox["b", RowBox[List["7", "/", "2"]]], " ", "c"]]]]]]]










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





2002-12-18