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 ArcSinh

 http://functions.wolfram.com/01.25.21.0014.01

 Input Form

 Integrate[Log[t] ArcSinh[t], {t, 0, 1}] == -2 + 2 Sqrt[2] - 2 ArcSinh[1] + Log[2]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List["Log", "[", "t", "]"]], " ", RowBox[List["ArcSinh", "[", "t", "]"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["2", " ", SqrtBox["2"]]], "-", RowBox[List["2", " ", RowBox[List["ArcSinh", "[", "1", "]"]]]], "+", RowBox[List["Log", "[", "2", "]"]]]]]]]]

 MathML Form

 0 1 log ( t ) sinh - 1 ( t ) t - 2 sinh - 1 ( 1 ) + log ( 2 ) + 2 2 - 2 t 0 1 t t -2 1 2 2 2 1 2 -2 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "1"], RowBox[List[RowBox[List[RowBox[List["Log", "[", "t_", "]"]], " ", RowBox[List["ArcSinh", "[", "t_", "]"]]]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "2"]], "+", RowBox[List["2", " ", SqrtBox["2"]]], "-", RowBox[List["2", " ", RowBox[List["ArcSinh", "[", "1", "]"]]]], "+", RowBox[List["Log", "[", "2", "]"]]]]]]]]

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

 2001-10-29