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Sinh






Mathematica Notation

Traditional Notation









Elementary Functions > Sinh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving products of sin > Involving sin(a z) sin(b z)sinh(c z)





http://functions.wolfram.com/01.19.21.0681.01









  


  










Input Form





Integrate[Sin[a z] Sin[b z] Sinh[c z], z] == (1/2) ((c Cos[(a - b) z] Cosh[c z])/(a^2 - 2 a b + b^2 + c^2) - (c Cos[(a + b) z] Cosh[c z])/(a^2 + 2 a b + b^2 + c^2) + ((a - b) Sin[(a - b) z] Sinh[c z])/(a^2 - 2 a b + b^2 + c^2) - ((a + b) Sin[(a + b) z] Sinh[c z])/(a^2 + 2 a b + b^2 + c^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[RowBox[List["Sin", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["b_", " ", "z_"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List["c", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", "a", " ", "b"]], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], "-", FractionBox[RowBox[List["c", " ", RowBox[List["Cos", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["2", " ", "a", " ", "b"]], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], "-", RowBox[List["2", " ", "a", " ", "b"]], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]], "-", FractionBox[RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", "z"]], "]"]]]], RowBox[List[SuperscriptBox["a", "2"], "+", RowBox[List["2", " ", "a", " ", "b"]], "+", SuperscriptBox["b", "2"], "+", SuperscriptBox["c", "2"]]]]]], ")"]]]]]]]]










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





2002-12-18