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SinhIntegral






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > SinhIntegral[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving elementary functions of the direct function > Involving products of the direct function





http://functions.wolfram.com/06.39.21.0049.01









  


  










Input Form





Integrate[SinhIntegral[a z] SinhIntegral[b z], z] == (1/(2 a b)) ((a - b) SinhIntegral[(a - b) z] - 2 b Cosh[a z] SinhIntegral[b z] - 2 a SinhIntegral[a z] (Cosh[b z] - b z SinhIntegral[b z]) + a SinhIntegral[(a + b) z] + b SinhIntegral[(a + b) z])










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a", " ", "b"]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]], "-", RowBox[List["b", " ", "z", " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], ")"]]]]]]]]










MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["SinhIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["SinhIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]], "-", RowBox[List["b", " ", "z", " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List["2", " ", "a", " ", "b"]]]]]]]










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





2001-10-29





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