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 Cosh

 http://functions.wolfram.com/01.20.21.1480.01

 Input Form

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

 Standard Form

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

 MathML Form

 sinh ( e + d z ) cosh ( c z ) z 1 8 ( e ( 4 - e cosh ( - z c + e + d z ) d + c c 2 4 d - 2 e π erfi ( c - 2 d z 2 - d ) ( - d ) 3 / 2 - c - c 2 4 d π erfi ( c - 2 d z 2 d ) d 3 / 2 ) - - e ( - 4 e cosh ( z c + e + d z ) d + c 2 e - c 2 4 d π erfi ( c + 2 d z 2 d ) d 3 / 2 - c c 2 4 d π erfi ( c + 2 d z 2 - d ) ( - d ) 3 / 2 ) ) z e d z c z 1 2 1 8 e 4 -1 e -1 z 1 2 c e d z d -1 c c 2 4 d -1 -1 2 e 1 2 Erfi c -1 2 d z 1 2 2 -1 d 1 2 -1 -1 d 3 2 -1 -1 c -1 c 2 4 d -1 1 2 Erfi c -1 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 -1 e -1 4 e z 1 2 c e d z d -1 c 2 e -1 c 2 4 d -1 1 2 Erfi c 2 d z 1 2 2 d 1 2 -1 d 3 2 -1 -1 c c 2 4 d -1 1 2 Erfi c 2 d z 1 2 2 -1 d 1 2 -1 -1 d 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[RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", SqrtBox["z_"]]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", "e"]]], " ", RowBox[List["Cosh", "[", RowBox[List["e", "-", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]]]], "d"], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]], "-", RowBox[List["2", " ", "e"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "d"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "-", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["d"]]]], "]"]]]], SuperscriptBox["d", RowBox[List["3", "/", "2"]]]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "e"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["4", " ", SuperscriptBox["\[ExponentialE]", "e"], " ", RowBox[List["Cosh", "[", RowBox[List["e", "+", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]]]], "d"]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["-", "d"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", "d"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", "d"]]]]], "+", RowBox[List["2", " ", "e"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox["d"]]]], "]"]]]], SuperscriptBox["d", RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]

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

 2002-12-18