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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and a power function > Involving exp and power > Involving zalpha-1 eb z+e sinh(c z)





http://functions.wolfram.com/01.19.21.0340.01









  


  










Input Form





Integrate[z^(7/2) E^(b z + e) Sinh[c z], z] == (1/2) E^e z^(9/2) ((1/((-b + c) z)^(9/2)) (E^((b - c) z) ((-b + c) z)^(7/2) + ((7/16) (15 E^(c z) Sqrt[Pi] + 2 E^(b z) Sqrt[(-b + c) z] (15 + 10 c z + 4 b^2 z^2 + 4 c^2 z^2 - 2 b z (5 + 4 c z)) - 15 E^(c z) Sqrt[Pi] Erf[Sqrt[(-b + c) z]]))/E^(c z)) - (1/((-(b + c)) z)^(9/2)) (E^((b + c) z) ((-(b + c)) z)^(7/2) + (7/16) (15 Sqrt[Pi] + 2 E^((b + c) z) Sqrt[(-(b + c)) z] (15 - 10 c z + 4 b^2 z^2 + 4 c^2 z^2 + 2 b z (-5 + 4 c z)) - 15 Sqrt[Pi] Erf[Sqrt[(-(b + c)) z]])))










Standard Form





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MathML Form







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</apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["z_", RowBox[List["7", "/", "2"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["b_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", SuperscriptBox["\[ExponentialE]", "e"], " ", SuperscriptBox["z", RowBox[List["9", "/", "2"]]], " ", RowBox[List["(", RowBox[List[FractionBox[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["7", "/", "2"]]]]], "+", RowBox[List[FractionBox["7", "16"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "c"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]], " ", SqrtBox["\[Pi]"]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", "b"]], "+", "c"]], ")"]], " ", "z"]]], " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["10", " ", "c", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "-", RowBox[List["2", " ", "b", " ", "z", " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["4", " ", "c", " ", "z"]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["15", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["c", " ", "z"]]], " ", 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["9", "/", "2"]]]], "-", FractionBox[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["7", "/", "2"]]]]], "+", RowBox[List[FractionBox["7", "16"], " ", RowBox[List["(", RowBox[List[RowBox[List["15", " ", 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["15", "-", RowBox[List["10", " ", "c", " ", "z"]], "+", RowBox[List["4", " ", SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["4", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List["2", " ", "b", " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "5"]], "+", RowBox[List["4", " ", "c", " ", "z"]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["15", " ", 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["9", "/", "2"]]]]]], ")"]]]]]]]]










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





2002-12-18