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CosIntegral






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/06.38.21.0041.01









  


  










Input Form





Integrate[z Cosh[b z] CosIntegral[a z], z] == (1/(4 b^2)) (ExpIntegralEi[((-I) a + b) z] + ExpIntegralEi[(I a + b) z] + ExpIntegralEi[(-I) a z - b z] + 4 CosIntegral[a z] (-Cosh[b z] + b z Sinh[b z]) + (1/(a^2 + b^2)) ((a^2 + b^2) ExpIntegralEi[I a z - b z] - 4 b (b Cos[a z] Cosh[b z] + a Sin[a z] Sinh[b 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["z_", " ", RowBox[List["Cosh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CosIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "a", " ", "z"]], "-", RowBox[List["b", " ", "z"]]]], "]"]], "+", RowBox[List["4", " ", RowBox[List["CosIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]], "-", RowBox[List["b", " ", "z"]]]], "]"]]]], "-", RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]]]], RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]]]]], RowBox[List["4", " ", SuperscriptBox["b", "2"]]]]]]]]










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





2001-10-29





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