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 ArcCsc

 http://functions.wolfram.com/01.17.21.0009.01

 Input Form

 Integrate[ArcCsc[t]/Sqrt[t], {t, 1, Infinity}] == -Pi + (Sqrt[Pi] Gamma[1/4])/Gamma[3/4]

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["ArcCsc", "[", "t", "]"]], SqrtBox["t"]], RowBox[List["\[DifferentialD]", "t"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]]]], RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]]]]]]]]]

 MathML Form

 1 csc - 1 ( t ) t t π Γ ( 1 4 ) Γ ( 3 4 ) - π t 1 t t 1 2 -1 1 2 Gamma 1 4 Gamma 3 4 -1 -1 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "1", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List["ArcCsc", "[", "t_", "]"]], SqrtBox["t_"]], RowBox[List["\[DifferentialD]", "t_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", "\[Pi]"]], "+", FractionBox[RowBox[List[SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", FractionBox["1", "4"], "]"]]]], RowBox[List["Gamma", "[", FractionBox["3", "4"], "]"]]]]]]]]]

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

 2001-10-29