URL: https://mathworld.wolfram.com/notebooks/Calculus/Integral.nb
(* Content-type: application/vnd.wolfram.mathematica *)
(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)
(* CreatedBy='Mathematica 9.0' *)
(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
NotebookDataLength[ 5286, 236]
NotebookOptionsPosition[ 3625, 170]
NotebookOutlinePosition[ 4169, 192]
CellTagsIndexPosition[ 4126, 189]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
Notebook[{
Cell[CellGroupData[{
Cell["Integral", "Title"],
Cell[CellGroupData[{
Cell["Author", "Subsection"],
Cell["\<\
Eric W. Weisstein
April 14, 2004\
\>", "Text"],
Cell[TextData[{
"This notebook downloaded from ",
ButtonBox["http://mathworld.wolfram.com/notebooks/Calculus/Integral.nb",
BaseStyle->"Hyperlink",
ButtonData:>{
URL["http://mathworld.wolfram.com/notebooks/Calculus/Integral.nb"], None}],
"."
}], "Text"],
Cell[TextData[{
"For more information, see Eric's ",
StyleBox["MathWorld",
FontSlant->"Italic"],
" entry ",
ButtonBox["http://mathworld.wolfram.com/Integral.html",
BaseStyle->"Hyperlink",
ButtonData:>{
URL["http://mathworld.wolfram.com/Integral.html"], None}],
"."
}], "Text"],
Cell["\<\
\[Copyright]2005 Wolfram Research, Inc. except for portions noted otherwise\
\>", "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell["Definite Intergal", "Section"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"f", "[", "x", "]"}], ",",
RowBox[{"{",
RowBox[{"x", ",", "a", ",", "b"}], "}"}]}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{
SubsuperscriptBox["\[Integral]", "a", "b"],
RowBox[{
RowBox[{"f", "[", "x", "]"}],
RowBox[{"\[DifferentialD]", "x"}]}]}]], "Output"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Indefinite Integral", "Section"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"f", "[", "x", "]"}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{"\[Integral]",
RowBox[{
RowBox[{"f", "[", "x", "]"}],
RowBox[{"\[DifferentialD]", "x"}]}]}]], "Output"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell["Cannot Be Done in Closed Form", "Section"],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"Exp", "[",
RowBox[{"-",
RowBox[{"x", "^", "2"}]}], "]"}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{
FractionBox["1", "2"], " ",
SqrtBox["\[Pi]"], " ",
RowBox[{"Erf", "[", "x", "]"}]}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"Exp", "[", "x", "]"}], "/", "x"}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{"ExpIntegralEi", "[", "x", "]"}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"Sin", "[", "x", "]"}], "/", "x"}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{"SinIntegral", "[", "x", "]"}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{
RowBox[{"Cos", "[", "x", "]"}], "/", "x"}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{"CosIntegral", "[", "x", "]"}]], "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[BoxData[
RowBox[{"Integrate", "[",
RowBox[{
RowBox[{"1", "/",
RowBox[{"Log", "[", "x", "]"}]}], ",", "x"}], "]"}]], "Input"],
Cell[BoxData[
RowBox[{"LogIntegral", "[", "x", "]"}]], "Output"]
}, Open ]]
}, Open ]]
}, Open ]]
},
WindowToolbars->{},
WindowSize->{520, 716},
WindowMargins->{{Automatic, 189}, {Automatic, 0}},
PrivateNotebookOptions->{"ColorPalette"->{RGBColor, -1}},
ShowCellLabel->True,
ShowCellTags->False,
RenderingOptions->{"ObjectDithering"->True,
"RasterDithering"->False},
FrontEndVersion->"9.0 for Mac OS X x86 (32-bit, 64-bit Kernel) (March 5, \
2013)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)
(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[579, 22, 25, 0, 92, "Title"],
Cell[CellGroupData[{
Cell[629, 26, 28, 0, 44, "Subsection"],
Cell[660, 28, 56, 3, 49, "Text"],
Cell[719, 33, 263, 7, 49, "Text"],
Cell[985, 42, 291, 10, 49, "Text"],
Cell[1279, 54, 99, 2, 49, "Text"]
}, Open ]],
Cell[CellGroupData[{
Cell[1415, 61, 36, 0, 80, "Section"],
Cell[CellGroupData[{
Cell[1476, 65, 173, 5, 28, "Input"],
Cell[1652, 72, 168, 5, 47, "Output"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[1869, 83, 38, 0, 80, "Section"],
Cell[CellGroupData[{
Cell[1932, 87, 114, 3, 28, "Input"],
Cell[2049, 92, 136, 4, 47, "Output"]
}, Open ]]
}, Open ]],
Cell[CellGroupData[{
Cell[2234, 102, 48, 0, 80, "Section"],
Cell[CellGroupData[{
Cell[2307, 106, 162, 5, 28, "Input"],
Cell[2472, 113, 127, 4, 47, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[2636, 122, 141, 4, 70, "Input"],
Cell[2780, 128, 67, 1, 70, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[2884, 134, 141, 4, 70, "Input"],
Cell[3028, 140, 65, 1, 70, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[3130, 146, 141, 4, 70, "Input"],
Cell[3274, 152, 65, 1, 70, "Output"]
}, Open ]],
Cell[CellGroupData[{
Cell[3376, 158, 141, 4, 70, "Input"],
Cell[3520, 164, 65, 1, 70, "Output"]
}, Open ]]
}, Open ]]
}, Open ]]
}
]
*)
(* End of internal cache information *)