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ExpIntegralEi






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > ExpIntegralEi[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions and a power function > Involving sinh and power





http://functions.wolfram.com/06.35.21.0043.01









  


  










Input Form





Integrate[z Sinh[b z] ExpIntegralEi[a z], z] == (1/(2 b^2)) (-ExpIntegralEi[(a - b) z] + ExpIntegralEi[(a + b) z] + 2 ExpIntegralEi[a z] (b z Cosh[b z] - Sinh[b z]) + (2 b E^(a z) ((-a) Cosh[b z] + b Sinh[b z]))/(a^2 - b^2))










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["z_", " ", RowBox[List["Sinh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["2", " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]], ")"]]]], "+", FractionBox[RowBox[List["2", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox["a", "2"], "-", SuperscriptBox["b", "2"]]]]]], RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]]]]]










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





2001-10-29





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