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variants of this functions
Erf






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > Erf[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving exponential function and trigonometric functions > Involving exp and sin





http://functions.wolfram.com/06.25.21.0051.01









  


  










Input Form





Integrate[E^(b z) Sin[c z] Erf[a z], z] == (1/(2 (b^2 + c^2))) (I E^((b - I c)^2/(4 a^2)) ((b + I c) Erf[(b - I c - 2 a^2 z)/(2 a)] - (b - I c) E^((I b c)/a^2) Erf[(b + I c - 2 a^2 z)/(2 a)]) + 2 E^(b z) Erf[a z] ((-c) Cos[c z] + b Sin[c z]))










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["\[ExponentialE]", RowBox[List["b_", " ", "z_"]]], " ", RowBox[List["Sin", "[", RowBox[List["c_", " ", "z_"]], "]"]], " ", RowBox[List["Erf", "[", RowBox[List["a_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], "2"], RowBox[List["4", " ", SuperscriptBox["a", "2"]]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], RowBox[List["2", " ", "a"]]], "]"]]]], "-", RowBox[List[RowBox[List["(", RowBox[List["b", "-", RowBox[List["\[ImaginaryI]", " ", "c"]]]], ")"]], " ", SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List["\[ImaginaryI]", " ", "b", " ", "c"]], SuperscriptBox["a", "2"]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List["b", "+", RowBox[List["\[ImaginaryI]", " ", "c"]], "-", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", "z"]]]], RowBox[List["2", " ", "a"]]], "]"]]]]]], ")"]]]], "+", RowBox[List["2", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["Erf", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["Cos", "[", RowBox[List["c", " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sin", "[", RowBox[List["c", " ", "z"]], "]"]]]]]], ")"]]]]]], RowBox[List["2", " ", RowBox[List["(", RowBox[List[SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]], ")"]]]]]]]]]










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





2001-10-29