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 Cosh

 http://functions.wolfram.com/01.20.21.0311.01

 Input Form

 Integrate[(E^(b z) Cosh[c z])/z^(9/2), z] == (1/(105 z^(7/2))) (-15 E^((b - c) z) - 15 E^((b + c) z) - 6 (b - c) E^((b - c) z) z - 6 (b + c) E^((b + c) z) z - 4 (b - c)^2 E^((b - c) z) z^2 - 4 (b + c)^2 E^((b + c) z) z^2 + 8 (-b + c)^3 E^((b - c) z) z^3 - 8 (b + c)^3 E^((b + c) z) z^3 - 8 Sqrt[Pi] ((-b + c) z)^(7/2) - 8 Sqrt[Pi] ((-(b + c)) z)^(7/2) + 8 Sqrt[Pi] ((-b + c) z)^(7/2) Erf[Sqrt[(-b + c) z]] + 8 Sqrt[Pi] ((-(b + c)) z)^(7/2) Erf[Sqrt[(-(b + c)) z]])

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SuperscriptBox["z", FractionBox["9", "2"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["105", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "15"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], "-", RowBox[List["15", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", "z"]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", "z"]], "-", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], "]"]]]], "+", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], "]"]]]]]], ")"]]]]]]]]

 MathML Form

 b z cosh ( c z ) z 9 / 2 z 1 105 z 7 / 2 ( 8 π erf ( ( c - b ) z ) ( ( c - b ) z ) 7 / 2 - 8 π ( ( c - b ) z ) 7 / 2 - 8 π ( - ( b + c ) z ) 7 / 2 - 15 ( b - c ) z - 15 ( b + c ) z + 8 ( c - b ) 3 ( b - c ) z z 3 - 8 ( b + c ) 3 ( b + c ) z z 3 - 4 ( b - c ) 2 ( b - c ) z z 2 - 4 ( b + c ) 2 ( b + c ) z z 2 - 6 ( b - c ) ( b - c ) z z - 6 ( b + c ) ( b + c ) z z + 8 π ( - ( b + c ) z ) 7 / 2 erf ( - ( b + c ) z ) ) z b z c z z 9 2 -1 1 105 z 7 2 -1 8 1 2 Erf c -1 b z 1 2 c -1 b z 7 2 -1 8 1 2 c -1 b z 7 2 -1 8 1 2 -1 b c z 7 2 -1 15 b -1 c z -1 15 b c z 8 c -1 b 3 b -1 c z z 3 -1 8 b c 3 b c z z 3 -1 4 b -1 c 2 b -1 c z z 2 -1 4 b c 2 b c z z 2 -1 6 b -1 c b -1 c z z -1 6 b c b c z z 8 1 2 -1 b c z 7 2 Erf -1 b c z 1 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], SuperscriptBox["z_", RowBox[List["9", "/", "2"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "15"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], "-", RowBox[List["15", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", "z"]], "-", RowBox[List["6", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", "z"]], "-", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["4", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8", " ", SuperscriptBox[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], "3"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SuperscriptBox["z", "3"]]], "-", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]], "-", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]], "+", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], "]"]]]], "+", RowBox[List["8", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], "]"]]]]]], RowBox[List["105", " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]]]]]]]]]

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

 2002-12-18