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 CoshIntegral

 http://functions.wolfram.com/06.40.21.0080.01

 Input Form

 Integrate[z SinhIntegral[b z] CoshIntegral[a z], z] == (-(1/(8 a^2 b^2))) ((-a) b E^((a - b) z) + a b E^((-a + b) z) + (a b)/E^((a + b) z) - a b E^((a + b) z) + (-(a^2 + b^2)) (ExpIntegralEi[(a - b) z] - ExpIntegralEi[(-a + b) z] + ExpIntegralEi[(-(a + b)) z] - ExpIntegralEi[(a + b) z]) - 2 b^2 (Gamma[2, (-a) z] + Gamma[2, a z]) SinhIntegral[b z] - 2 a^2 CoshIntegral[a z] (Gamma[2, (-b) z] - Gamma[2, b z] + 2 b^2 z^2 SinhIntegral[b z]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["8", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], " ", "z"]]]]], "-", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]]]], " ", 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[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "a"]], " ", "z"]]]], "]"]], "+", RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List["a", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "b"]], " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List["b", " ", "z"]]]], "]"]], "+", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 z Shi ( b z ) Chi ( a z ) z - 1 8 a 2 b 2 ( - 2 Chi ( a z ) ( 2 b 2 Shi ( b z ) z 2 + Γ ( 2 , - b z ) - Γ ( 2 , b z ) ) a 2 + b ( b - a ) z a + b - ( a + b ) z a - b ( a + b ) z a - a b ( a - b ) z - ( a 2 + b 2 ) ( Ei ( ( a - b ) z ) - Ei ( ( b - a ) z ) + Ei ( - ( a + b ) z ) - Ei ( ( a + b ) z ) ) - 2 b 2 ( Γ ( 2 , - a z ) + Γ ( 2 , a z ) ) Shi ( b z ) ) z z SinhIntegral b z CoshIntegral a z -1 1 8 a 2 b 2 -1 -2 CoshIntegral a z 2 b 2 SinhIntegral b z z 2 Gamma 2 -1 b z -1 Gamma 2 b z a 2 b b -1 a z a b -1 a b z a -1 b a b z a -1 a b a -1 b z -1 a 2 b 2 ExpIntegralEi a -1 b z -1 ExpIntegralEi b -1 a z ExpIntegralEi -1 a b z -1 ExpIntegralEi a b z -1 2 b 2 Gamma 2 -1 a z Gamma 2 a z SinhIntegral b z [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List["z_", " ", RowBox[List["SinhIntegral", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], " ", "z"]]]]], "-", RowBox[List["a", " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]]]], "-", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", 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[RowBox[List["-", "a"]], "+", "b"]], ")"]], " ", "z"]], "]"]], "+", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]]]], " ", "z"]], "]"]], "-", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], ")"]]]], "-", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "a"]], " ", "z"]]]], "]"]], "+", RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List["a", " ", "z"]]]], "]"]]]], ")"]], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List[RowBox[List["-", "b"]], " ", "z"]]]], "]"]], "-", RowBox[List["Gamma", "[", RowBox[List["2", ",", RowBox[List["b", " ", "z"]]]], "]"]], "+", RowBox[List["2", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["SinhIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]]]], RowBox[List["8", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]]]]]]]]]

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

 2001-10-29