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 SinIntegral

 http://functions.wolfram.com/06.37.21.0043.01

 Input Form

 Integrate[z^2 Cosh[b z] SinIntegral[a z], z] == (-(1/(4 b^3))) (I ((1/(a^2 + b^2)^2) (2 (a^2 + b^2)^2 (ExpIntegralEi[((-I) a + b) z] - ExpIntegralEi[(I a + b) z] - ExpIntegralEi[(-I) a z - b z] + ExpIntegralEi[I a z - b z]) - 4 I b^2 Sin[a z] (b (a^2 + b^2) z Cosh[b z] - (a^2 + 3 b^2) Sinh[b z]) + 4 I a b Cos[a z] (-2 (a^2 + 2 b^2) Cosh[b z] + b (a^2 + b^2) z Sinh[b z])) + 2 I (Gamma[3, (-b) z] - Gamma[3, b z]) SinIntegral[a z]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", "2"], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["4", " ", SuperscriptBox["b", "3"]]]]]], RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], "2"]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], "2"], " ", RowBox[List["(", 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["ExpIntegralEi", "[", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "a", " ", "z"]], "-", RowBox[List["b", " ", "z"]]]], "]"]]]], ")"]]]], "-", RowBox[List["4", " ", "\[ImaginaryI]", " ", SuperscriptBox["b", "2"], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["3", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List["4", " ", "\[ImaginaryI]", " ", "a", " ", "b", " ", RowBox[List["Cos", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["2", " ", SuperscriptBox["b", "2"]]]]], ")"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", "z", " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List[RowBox[List["-", "b"]], " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["3", ",", RowBox[List["b", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinIntegral", "[", RowBox[List["a", " ", "z"]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 z 2 cosh ( b z ) Si ( a z ) z - 1 4 b 3 ( ( 1 ( a 2 + b 2 ) 2 ( - 4 sin ( a z ) ( b ( a 2 + b 2 ) z cosh ( b z ) - ( a 2 + 3 b 2 ) sinh ( b z ) ) b 2 + 4 a cos ( a z ) ( b ( a 2 + b 2 ) z sinh ( b z ) - 2 ( a 2 + 2 b 2 ) cosh ( b z ) ) b + 2 ( a 2 + b 2 ) 2 ( Ei ( ( b - a ) z ) - Ei ( ( b + a ) z ) - Ei ( - b z + a ( - ) z ) + Ei ( a z - b z ) ) ) + 2 ( Γ ( 3 , - b z ) - Γ ( 3 , b z ) ) Si ( a z ) ) ) z z 2 b z SinIntegral a z -1 1 4 b 3 -1 1 a 2 b 2 2 -1 -4 a z b a 2 b 2 z b z -1 a 2 3 b 2 b z b 2 4 a a z b a 2 b 2 z b z -1 2 a 2 2 b 2 b z b 2 a 2 b 2 2 ExpIntegralEi b -1 a z -1 ExpIntegralEi b a z -1 ExpIntegralEi -1 b z a -1 z ExpIntegralEi a z -1 b z 2 Gamma 3 -1 b z -1 Gamma 3 b z SinIntegral a z [/itex]

 Rule Form

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

 2001-10-29