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 Cosh

 http://functions.wolfram.com/01.20.21.0304.01

 Input Form

 Integrate[z^(5/2) E^(b z) Cosh[c z], z] == (1/2) z^(7/2) ((1/((-b + c) z)^(7/2)) ((-E^((b - c) z)) ((-b + c) z)^(5/2) + (5/8) (-3 Sqrt[Pi] + 2 E^((b - c) z) Sqrt[(-b + c) z] (-3 + 2 b z - 2 c z) + 3 Sqrt[Pi] Erf[Sqrt[(-b + c) z]])) + (1/((-(b + c)) z)^(7/2)) ((-E^((b + c) z)) ((-(b + c)) z)^(5/2) + (5/8) (-3 Sqrt[Pi] + 2 E^((b + c) z) Sqrt[(-(b + c)) z] (-3 + 2 b z + 2 c z) + 3 Sqrt[Pi] Erf[Sqrt[(-(b + c)) z]])))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[SuperscriptBox["z", FractionBox["5", "2"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[FractionBox["5", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SqrtBox["\[Pi]"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]], "+", RowBox[List["3", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], "]"]]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List[FractionBox["1", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[FractionBox["5", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SqrtBox["\[Pi]"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]], "+", RowBox[List["3", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], "]"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]]]]

 MathML Form

 z 5 / 2 b z cosh ( c z ) z 1 2 z 7 / 2 ( 1 ( ( c - b ) z ) 7 / 2 ( 5 8 ( 2 ( b - c ) z ( c - b ) z ( 2 b z - 2 c z - 3 ) + 3 π erf ( ( c - b ) z ) - 3 π ) - ( b - c ) z ( ( c - b ) z ) 5 / 2 ) + 1 ( - ( b + c ) z ) 7 / 2 ( 5 8 ( 2 ( b + c ) z - ( b + c ) z ( 2 b z + 2 c z - 3 ) + 3 π erf ( - ( b + c ) z ) - 3 π ) - ( b + c ) z ( - ( b + c ) z ) 5 / 2 ) ) z z 5 2 b z c z 1 2 z 7 2 1 c -1 b z 7 2 -1 5 8 2 b -1 c z c -1 b z 1 2 2 b z -1 2 c z -3 3 1 2 Erf c -1 b z 1 2 -1 3 1 2 -1 b -1 c z c -1 b z 5 2 1 -1 b c z 7 2 -1 5 8 2 b c z -1 b c z 1 2 2 b z 2 c z -3 3 1 2 Erf -1 b c z 1 2 -1 3 1 2 -1 b c z -1 b c z 5 2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["5", "/", "2"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["z", RowBox[List["7", "/", "2"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[FractionBox["5", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SqrtBox["\[Pi]"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]], "+", RowBox[List["3", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], "]"]]]]]], ")"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List[FractionBox["5", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "3"]], " ", SqrtBox["\[Pi]"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "3"]], "+", RowBox[List["2", " ", "b", " ", "z"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]], "+", RowBox[List["3", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], "]"]]]]]], ")"]]]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["7", "/", "2"]]]]]], ")"]]]]]]]]

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

 2002-12-18