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 Cos

 http://functions.wolfram.com/01.07.21.0017.01

 Input Form

 Integrate[(Cos[a t] - Cos[b t])/t, {t, 0, Infinity}] == (1/2) Log[b^2/a^2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["a", " ", "t"]], "]"]], "-", RowBox[List["Cos", "[", RowBox[List["b", " ", "t"]], "]"]]]], "t"], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]], "]"]]]]]]]]

 MathML Form

 0 cos ( a t ) - cos ( b t ) t t 1 2 log ( b 2 a 2 ) t 0 a t -1 b t t -1 1 2 b 2 a 2 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Cos", "[", RowBox[List["a_", " ", "t_"]], "]"]], "-", RowBox[List["Cos", "[", RowBox[List["b_", " ", "t_"]], "]"]]]], "t_"], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox["1", "2"], " ", RowBox[List["Log", "[", FractionBox[SuperscriptBox["b", "2"], SuperscriptBox["a", "2"]], "]"]]]]]]]]

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

 2001-10-29