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Cosh




Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic and exponential functions > Involving sinh and exp > Involving ep zrsinh(b z)cosh(c z)





http://functions.wolfram.com/01.20.21.1818.01









  


  








Input Form





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








Standard Form





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MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["p_", " ", SqrtBox["z_"]]]], " ", RowBox[List["Sinh", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["8", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["p", " ", SqrtBox["z"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List["b", " ", RowBox[List["Cosh", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], "-", RowBox[List["c", " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]], " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "c"]], "+", RowBox[List["4", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List[RowBox[List["4", " ", "c"]], "-", RowBox[List["4", " ", "b"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "b"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "+", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "+", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "-", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["-", "c"]], "-", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "c"]], "-", "b"]], ")"]], RowBox[List["3", "/", "2"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox[SuperscriptBox["p", "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]]]]]]]], " ", "p", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["p", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]], " ", SqrtBox["z"]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["c", "+", "b"]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List["c", "+", "b"]], ")"]], RowBox[List["3", "/", "2"]]]]]], ")"]]]]]]]]


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





2002-12-18