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 Cosh

 http://functions.wolfram.com/01.20.21.1508.01

 Input Form

 Integrate[Sinh[d z + e] Cosh[c Sqrt[z] + f z], z] == (1/8) (E^e ((4 Cosh[e - c Sqrt[z] + (d - f) z])/(E^e (d - f)) - (c Sqrt[Pi] Erfi[(c + 2 (-d + f) Sqrt[z])/(2 Sqrt[d - f])])/ (E^(c^2/(4 (d - f))) (d - f)^(3/2)) + (c E^(-2 e - c^2/(4 (-d + f))) Sqrt[Pi] Erfi[(c + 2 (-d + f) Sqrt[z])/(2 Sqrt[-d + f])])/(-d + f)^(3/2)) - (-((4 E^e Cosh[e + c Sqrt[z] + (d + f) z])/(d + f)) - (c Sqrt[Pi] Erfi[(c + 2 (d + f) Sqrt[z])/(2 Sqrt[-d - f])])/ (E^(c^2/(4 (-d - f))) (-d - f)^(3/2)) + (c E^(2 e - c^2/(4 (d + f))) Sqrt[Pi] Erfi[(c + 2 (d + f) Sqrt[z])/ (2 Sqrt[d + f])])/(d + f)^(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[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "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[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]]], "]"]]]], RowBox[List["d", "-", "f"]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "-", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "2"]], " ", "e"]], "-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "f"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "d"]], "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "f"]], ")"]], 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[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", "z"]]]], "]"]]]], RowBox[List["d", "+", "f"]]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", "f"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "d"]], "-", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "-", "f"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "e"]], "-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["c", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["d", "+", "f"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

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

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

 2002-12-18