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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function > Involving exp > Involving ab zr+d z cosh(f z+g)





http://functions.wolfram.com/01.20.21.0204.01









  


  










Input Form





Integrate[a^(b z^2 + d z) Cosh[f z + g], z] == (1/(4 Sqrt[b Log[a]])) ((E^(f^2/(4 b Log[a])) Sqrt[Pi] (E^((d f)/b) Erfi[(-f + (d + 2 b z) Log[a])/(2 Sqrt[b Log[a]])] (Cosh[g] - Sinh[g]) + Erfi[(f + (d + 2 b z) Log[a])/(2 Sqrt[b Log[a]])] (Cosh[g] + Sinh[g])))/a^((2 f^2 + 2 d f Log[a] + d^2 Log[a]^2)/ (4 b Log[a]^2)))










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["a_", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]]]]], " ", RowBox[List["Cosh", "[", RowBox[List[RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["a", RowBox[List["-", FractionBox[RowBox[List[RowBox[List["2", " ", SuperscriptBox["f", "2"]]], "+", RowBox[List["2", " ", "d", " ", "f", " ", RowBox[List["Log", "[", "a", "]"]]]], "+", RowBox[List[SuperscriptBox["d", "2"], " ", SuperscriptBox[RowBox[List["Log", "[", "a", "]"]], "2"]]]]], RowBox[List["4", " ", "b", " ", SuperscriptBox[RowBox[List["Log", "[", "a", "]"]], "2"]]]]]]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["f", "2"], RowBox[List["4", " ", "b", " ", RowBox[List["Log", "[", "a", "]"]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["d", " ", "f"]], "b"]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["-", "f"]], "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", "a", "]"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "g", "]"]], "-", RowBox[List["Sinh", "[", "g", "]"]]]], ")"]]]], "+", RowBox[List[RowBox[List["Erfi", "[", FractionBox[RowBox[List["f", "+", RowBox[List[RowBox[List["(", RowBox[List["d", "+", RowBox[List["2", " ", "b", " ", "z"]]]], ")"]], " ", RowBox[List["Log", "[", "a", "]"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["Cosh", "[", "g", "]"]], "+", RowBox[List["Sinh", "[", "g", "]"]]]], ")"]]]]]], ")"]]]], RowBox[List["4", " ", SqrtBox[RowBox[List["b", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]]]]










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





2002-12-18