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 Cosh

 http://functions.wolfram.com/01.20.21.0346.01

 Input Form

 Integrate[(E^(b z + e) Cosh[c z])/z^(7/2), z] == (-(1/(15 z^(5/2)))) (E^e (3 E^((b - c) z) + 3 E^((b + c) z) + 2 (b - c) E^((b - c) z) z + 2 (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 - 4 Sqrt[Pi] ((-b + c) z)^(5/2) - 4 Sqrt[Pi] ((-(b + c)) z)^(5/2) + 4 Sqrt[Pi] ((-b + c) z)^(5/2) Erf[Sqrt[(-b + c) z]] + 4 Sqrt[Pi] ((-(b + c)) z)^(5/2) Erf[Sqrt[(-(b + c)) z]]))

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b", " ", "z"]], "+", "e"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], SuperscriptBox["z", FractionBox["7", "2"]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["15", " ", SuperscriptBox["z", RowBox[List["5", "/", "2"]]]]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], " ", RowBox[List["(", RowBox[List[RowBox[List["3", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]]]], "+", RowBox[List["3", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]]], "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", "z"]]], " ", "z"]], "+", RowBox[List["2", " ", 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["4", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "-", RowBox[List["4", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]]]], "+", RowBox[List["4", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], "]"]]]], "+", RowBox[List["4", " ", SqrtBox["\[Pi]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]], ")"]], RowBox[List["5", "/", "2"]]], " ", RowBox[List["Erf", "[", SqrtBox[RowBox[List[RowBox[List["-", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]], " ", "z"]]], "]"]]]]]], ")"]]]], ")"]]]]]]]]

 MathML Form

 e + b z cosh ( c z ) z 7 / 2 z - 1 15 z 5 / 2 ( e ( 4 π erf ( ( c - b ) z ) ( ( c - b ) z ) 5 / 2 - 4 π ( ( c - b ) z ) 5 / 2 - 4 π ( - ( b + c ) z ) 5 / 2 + 3 ( b - c ) z + 3 ( b + c ) z + 4 ( b - c ) 2 ( b - c ) z z 2 + 4 ( b + c ) 2 ( b + c ) z z 2 + 2 ( b - c ) ( b - c ) z z + 2 ( b + c ) ( b + c ) z z + 4 π ( - ( b + c ) z ) 5 / 2 erf ( - ( b + c ) z ) ) ) z e b z c z z 7 2 -1 -1 1 15 z 5 2 -1 e 4 1 2 Erf c -1 b z 1 2 c -1 b z 5 2 -1 4 1 2 c -1 b z 5 2 -1 4 1 2 -1 b c z 5 2 3 b -1 c z 3 b c z 4 b -1 c 2 b -1 c z z 2 4 b c 2 b c z z 2 2 b -1 c b -1 c z z 2 b c b c z z 4 1 2 -1 b c z 5 2 Erf -1 b c z 1 2 [/itex]

 Rule Form

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

 2002-12-18