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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0068.01

 Input Form

 Integrate[z^2 ExpIntegralEi[b z] CoshIntegral[a z], z] == (1/3) (((a^2 + 2 b^2) E^(b z) Cosh[a z])/(a^2 (a - b) b (a + b)) - (E^(b z) (2 - 2 b z + b^2 z^2) CoshIntegral[a z])/b^3 + (1/(a^3 b^3)) ((a^3 - b^3) ExpIntegralEi[(-a + b) z] + (a^3 + b^3) ExpIntegralEi[(a + b) z]) - (E^(b z) (a^2 (2 - b z) + b^2 (1 + b z)) Sinh[a z])/ (a (a - b) b^2 (a + b)) + (1/a^3) (ExpIntegralEi[b z] (2 a z Cosh[a z] + a^3 z^3 CoshIntegral[a z] - (2 + a^2 z^2) Sinh[a z])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "3"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "b", " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], SuperscriptBox["b", "3"]], "+", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["b", "3"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "-", SuperscriptBox["b", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "3"], "+", SuperscriptBox["b", "3"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], ")"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["2", "-", RowBox[List["b", " ", "z"]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["b", " ", "z"]]]], ")"]]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]], RowBox[List["a", " ", RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox["a", "3"]], RowBox[List["(", RowBox[List[RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "3"], " ", SuperscriptBox["z", "3"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["2", "+", RowBox[List[SuperscriptBox["a", "2"], " ", SuperscriptBox["z", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 z 2 Ei ( b z ) Chi ( a z ) z 1 3 ( ( a 2 + 2 b 2 ) b z cosh ( a z ) a 2 ( a - b ) b ( a + b ) + ( a 3 - b 3 ) Ei ( ( b - a ) z ) + ( a 3 + b 3 ) Ei ( ( a + b ) z ) a 3 b 3 + 1 a 3 ( Ei ( b z ) ( a 3 Chi ( a z ) z 3 + 2 a cosh ( a z ) z - ( a 2 z 2 + 2 ) sinh ( a z ) ) ) - b z ( b 2 z 2 - 2 b z + 2 ) Chi ( a z ) b 3 - b z ( ( 2 - b z ) a 2 + b 2 ( b z + 1 ) ) sinh ( a z ) a ( a - b ) b 2 ( a + b ) ) z z 2 ExpIntegralEi b z CoshIntegral a z 1 3 a 2 2 b 2 b z a z a 2 a -1 b b a b -1 a 3 -1 b 3 ExpIntegralEi b -1 a z a 3 b 3 ExpIntegralEi a b z a 3 b 3 -1 1 a 3 -1 ExpIntegralEi b z a 3 CoshIntegral a z z 3 2 a a z z -1 a 2 z 2 2 a z -1 b z b 2 z 2 -1 2 b z 2 CoshIntegral a z b 3 -1 -1 b z 2 -1 b z a 2 b 2 b z 1 a z a a -1 b b 2 a b -1 [/itex]

 Rule Form

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

 2001-10-29