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 Cosh

 http://functions.wolfram.com/01.20.21.1478.01

 Input Form

 Integrate[Sinh[b z] Cosh[c Sqrt[z]], z] == (1/8) ((8 Cosh[c Sqrt[z]] Cosh[b z])/b + (c E^(c^2/(4 b)) Sqrt[Pi] Erfi[(c - 2 b Sqrt[z])/(2 Sqrt[-b])])/ (-b)^(3/2) - (c Sqrt[Pi] Erfi[(c - 2 b Sqrt[z])/(2 Sqrt[b])])/ (E^(c^2/(4 b)) b^(3/2)) + (c E^(c^2/(4 b)) Sqrt[Pi] Erfi[(c + 2 b Sqrt[z])/(2 Sqrt[-b])])/(-b)^(3/2) - (c Sqrt[Pi] Erfi[(c + 2 b Sqrt[z])/(2 Sqrt[b])])/(E^(c^2/(4 b)) b^(3/2)))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "b"], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["b"]]]], "]"]]]], SuperscriptBox["b", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["b"]]]], "]"]]]], SuperscriptBox["b", RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

 MathML Form

 sinh ( b z ) cosh ( c z ) z 1 8 ( 8 cosh ( c z ) cosh ( b z ) b + c c 2 4 b π erfi ( 2 z b + c 2 - b ) ( - b ) 3 / 2 + c c 2 4 b π erfi ( c - 2 b z 2 - b ) ( - b ) 3 / 2 - c - c 2 4 b π erfi ( 2 z b + c 2 b ) b 3 / 2 - c - c 2 4 b π erfi ( c - 2 b z 2 b ) b 3 / 2 ) z b z c z 1 2 1 8 8 c z 1 2 b z b -1 c c 2 4 b -1 1 2 Erfi 2 z 1 2 b c 2 -1 b 1 2 -1 -1 b 3 2 -1 c c 2 4 b -1 1 2 Erfi c -1 2 b z 1 2 2 -1 b 1 2 -1 -1 b 3 2 -1 -1 c -1 c 2 4 b -1 1 2 Erfi 2 z 1 2 b c 2 b 1 2 -1 b 3 2 -1 -1 c -1 c 2 4 b -1 1 2 Erfi c -1 2 b z 1 2 2 b 1 2 -1 b 3 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[RowBox[List["Sinh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SqrtBox["z"]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "b"], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["b"]]]], "]"]]]], SuperscriptBox["b", RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "b"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "b", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["b"]]]], "]"]]]], SuperscriptBox["b", RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]

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

 2002-12-18