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 Cosh

 http://functions.wolfram.com/01.20.21.1526.01

 Input Form

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

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b", " ", SqrtBox["z"]]], "+", RowBox[List["d", " ", "z"]]]], "]"]], RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]], "+", "g"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "g"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f"]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "g"]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "d"]], "+", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List[RowBox[List["-", "d"]], "+", "f"]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "b"]], "+", "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[RowBox[List["(", 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FractionBox[RowBox[List["b", "+", "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[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]]]]]]], "+", RowBox[List["2", " ", "g"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["b", "+", "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 ( z b + d z ) cosh ( z c + g + f z ) z 1 8 ( - g ( - ( c - b ) - ( b - c ) 2 4 ( d - f ) π erfi ( - b + c + 2 ( f - d ) z 2 d - f ) ( d - f ) 3 / 2 + ( c - b ) 2 g - ( c - b ) 2 4 ( f - d ) π erfi ( - b + c + 2 ( f - d ) z 2 f - d ) ( f - d ) 3 / 2 + 2 z ( b - c ) + ( d - f ) z d - f - 2 z ( c - b ) + 2 g + ( f - d ) z f - d ) - - g ( - ( b + c ) - ( - b - c ) 2 4 ( - d - f ) π erfi ( b + c + 2 ( d + f ) z 2 - d - f ) ( - d - f ) 3 / 2 + ( b + c ) 2 g - ( b + c ) 2 4 ( d + f ) π erfi ( b + c + 2 ( d + f ) z 2 d + f ) ( d + f ) 3 / 2 + 2 z ( - b - c ) + ( - d - f ) z - d - f - 2 z ( b + c ) + 2 g + ( d + f ) z d + f ) ) z z 1 2 b d z z 1 2 c g f z 1 8 -1 g -1 c -1 b -1 b -1 c 2 4 d -1 f -1 1 2 Erfi -1 b c 2 f -1 d z 1 2 2 d -1 f 1 2 -1 d -1 f 3 2 -1 c -1 b 2 g -1 c -1 b 2 4 f -1 d -1 1 2 Erfi -1 b c 2 f -1 d z 1 2 2 f -1 d 1 2 -1 f -1 d 3 2 -1 2 z 1 2 b -1 c d -1 f z d -1 f -1 -1 2 z 1 2 c -1 b 2 g f -1 d z f -1 d -1 -1 -1 g -1 b c -1 -1 b -1 c 2 4 -1 d -1 f -1 1 2 Erfi b c 2 d f z 1 2 2 -1 d -1 f 1 2 -1 -1 d -1 f 3 2 -1 b c 2 g -1 b c 2 4 d f -1 1 2 Erfi b c 2 d f z 1 2 2 d f 1 2 -1 d f 3 2 -1 2 z 1 2 -1 b -1 c -1 d -1 f z -1 d -1 f -1 -1 2 z 1 2 b c 2 g d f z d f -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["b_", " ", SqrtBox["z_"]]], "+", RowBox[List["d_", " ", "z_"]]]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "g"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SqrtBox["z"]]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], " ", "z"]]]]]]], RowBox[List["d", "-", "f"]]], "-", FractionBox[RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " 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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