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Sinh




Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of the direct function > Involving products of two direct functions > Involving sinh(b zr+d z+e) sinh(c zr+f z+g)





http://functions.wolfram.com/01.19.21.1527.01









  


  








Input Form





Integrate[Sinh[b z^2 + d z + e] Sinh[c z^2 + f z + g], z] == (1/8) Sqrt[Pi] ((E^((d^2 - 4 c e + 2 d f + f^2 - 4 c g - 4 b (e + g))/(4 (b + c))) Erf[(d + f + 2 (b + c) z)/(2 Sqrt[b + c])])/Sqrt[b + c] - (E^(e - (d - f)^2/(4 (b - c)) - g) Erfi[(d - f + 2 b z - 2 c z)/ (2 Sqrt[b - c])])/Sqrt[b - c] + (E^(e - (d + f)^2/(4 (b + c)) + g) Erfi[(d + f + 2 (b + c) z)/ (2 Sqrt[b + c])])/Sqrt[b + c] - (E^(-e + (d - f)^2/(4 (b - c)) + g) Erf[(d - f + 2 b z - 2 c z)/ (2 Sqrt[b - c])])/Sqrt[b - c])








Standard Form





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MathML Form







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</apply> <cn type='integer'> -1 </cn> </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[RowBox[List["Sinh", "[", RowBox[List[RowBox[List["b_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["d_", " ", "z_"]], "+", "e_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List[RowBox[List["c_", " ", SuperscriptBox["z_", "2"]]], "+", RowBox[List["f_", " ", "z_"]], "+", "g_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "8"], " ", SqrtBox["\[Pi]"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", FractionBox[RowBox[List[SuperscriptBox["d", "2"], "-", RowBox[List["4", " ", "c", " ", "e"]], "+", RowBox[List["2", " ", "d", " ", "f"]], "+", SuperscriptBox["f", "2"], "-", RowBox[List["4", " ", "c", " ", "g"]], "-", RowBox[List["4", " ", "b", " ", RowBox[List["(", RowBox[List["e", "+", "g"]], ")"]]]]]], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List["d", "+", "f", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "+", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List["b", "+", "c"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]]]]], "-", "g"]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["d", "-", "f", "+", RowBox[List["2", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "-", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List["b", "-", "c"]]]], "+", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["e", "-", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "+", "f"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]]]]], "+", "g"]]], " ", RowBox[List["Erfi", "[", FractionBox[RowBox[List["d", "+", "f", "+", RowBox[List["2", " ", RowBox[List["(", RowBox[List["b", "+", "c"]], ")"]], " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "+", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List["b", "+", "c"]]]], "-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", "e"]], "+", FractionBox[SuperscriptBox[RowBox[List["(", RowBox[List["d", "-", "f"]], ")"]], "2"], RowBox[List["4", " ", RowBox[List["(", RowBox[List["b", "-", "c"]], ")"]]]]], "+", "g"]]], " ", RowBox[List["Erf", "[", FractionBox[RowBox[List["d", "-", "f", "+", RowBox[List["2", " ", "b", " ", "z"]], "-", RowBox[List["2", " ", "c", " ", "z"]]]], RowBox[List["2", " ", SqrtBox[RowBox[List["b", "-", "c"]]]]]], "]"]]]], SqrtBox[RowBox[List["b", "-", "c"]]]]]], ")"]]]]]]]]


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





2002-12-18