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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Arguments involving polynomials or algebraic functions and factors involving exponential functions > Involving exp > Involving ad z sin(c zr+f z+g)





http://functions.wolfram.com/01.06.21.0570.01









  


  










Input Form





Integrate[a^(d z) Sin[c Sqrt[z] + f z + g], z] == ((-(1/4)) I (-((I c E^(c^2/(-4 I f + 4 d Log[a])) Sqrt[Pi] Erfi[((-I) (c + 2 f Sqrt[z]) + 2 d Sqrt[z] Log[a])/ (2 Sqrt[(-I) f + d Log[a]])])/((-I) f + d Log[a])^(3/2)) - (I c E^(2 I g + c^2/(4 I f + 4 d Log[a])) Sqrt[Pi] Erfi[(I c + 2 Sqrt[z] (I f + d Log[a]))/(2 Sqrt[I f + d Log[a]])])/ (I f + d Log[a])^(3/2) - (2 I a^(d z) (E^(2 I (g + c Sqrt[z] + f z))/(f - I d Log[a]) + 1/(f + I d Log[a])))/E^(I (c Sqrt[z] + f z))))/E^(I g)










Standard Form





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MathML Form







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










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[RowBox[List[SuperscriptBox["a_", RowBox[List["d_", " ", "z_"]]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["c_", " ", SqrtBox["z_"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox["1", "4"]]], " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "g"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "c", " ", SuperscriptBox["\[ExponentialE]", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List[RowBox[List["-", "4"]], " ", "\[ImaginaryI]", " ", "f"]], "+", RowBox[List["4", " ", "d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List["c", "+", RowBox[List["2", " ", "f", " ", SqrtBox["z"]]]]], ")"]]]], "+", RowBox[List["2", " ", "d", " ", SqrtBox["z"], " ", RowBox[List["Log", "[", "a", "]"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "f"]], "+", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", "f"]], "+", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]]]], "-", FractionBox[RowBox[List["\[ImaginaryI]", " ", "c", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["2", " ", "\[ImaginaryI]", " ", "g"]], "+", FractionBox[SuperscriptBox["c", "2"], RowBox[List[RowBox[List["4", " ", "\[ImaginaryI]", " ", "f"]], "+", RowBox[List["4", " ", "d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "c"]], "+", RowBox[List["2", " ", SqrtBox["z"], " ", RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "f"]], "+", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]]]]]], RowBox[List["2", " ", SqrtBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", "f"]], "+", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]]], "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", "f"]], "+", RowBox[List["d", " ", RowBox[List["Log", "[", "a", "]"]]]]]], ")"]], RowBox[List["3", "/", "2"]]]], "-", RowBox[List["2", " ", "\[ImaginaryI]", " ", SuperscriptBox["a", RowBox[List["d", " ", "z"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]], ")"]]]]], " ", RowBox[List["(", RowBox[List[FractionBox[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "\[ImaginaryI]", " ", RowBox[List["(", RowBox[List["g", "+", RowBox[List["c", " ", SqrtBox["z"]]], "+", RowBox[List["f", " ", "z"]]]], ")"]]]]], RowBox[List["f", "-", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]], "+", FractionBox["1", RowBox[List["f", "+", RowBox[List["\[ImaginaryI]", " ", "d", " ", RowBox[List["Log", "[", "a", "]"]]]]]]]]], ")"]]]]]], ")"]]]]]]]]










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





2002-12-18