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 Cosh

 http://functions.wolfram.com/01.20.21.0484.01

 Input Form

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

 Standard Form

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

 e + d z cosh ( z c + g + f z ) z 1 4 e - g ( c c 2 4 f - 4 d π erfi ( 2 ( d - f ) z - c 2 d - f ) ( d - f ) 3 / 2 - 2 d z - f z - c z f - d + 2 z c + 2 g + ( d + f ) z d + f - c 2 g - 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 g f z 1 4 e -1 g c c 2 4 f -1 4 d -1 1 2 Erfi 2 d -1 f z 1 2 -1 c 2 d -1 f 1 2 -1 d -1 f 3 2 -1 -1 2 d z -1 f z -1 c z 1 2 f -1 d -1 2 z 1 2 c 2 g d f z d f -1 -1 c 2 g -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 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["d_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", "g"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]], "-", RowBox[List["f", " ", "z"]]]]]]], RowBox[List[RowBox[List["-", "d"]], "+", "f"]]]]], "+", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "+", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "+", "f"]]], "+", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "d"]], "+", RowBox[List["4", " ", "f"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[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"]]]], "-", FractionBox[RowBox[List["c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox["c", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g"]]]]], " ", 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