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Plot[{\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "sin integral", WolframAlphaClient`Private`boxes$$ = RowBox[{"SinIntegral", "[", "x", "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "MultiClash", "word" -> "", "count" -> "2", "Values" -> {{ "name" -> "Function", "word" -> "the input", "desc" -> "a math function", "input" -> "*MC.%7E-_*Function-"}, { "name" -> "MathWorld", "word" -> "sin", "desc" -> "referring to a definition", "input" -> "*MC.%7E-_*MathWorld-"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{113., {12., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), \!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "sin integral", WolframAlphaClient`Private`boxes$$ = RowBox[{"SinIntegral", "[", "x", "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "MultiClash", "word" -> "", "count" -> "2", "Values" -> {{ "name" -> "Function", "word" -> "the input", "desc" -> "a math function", "input" -> "*MC.%7E-_*Function-"}, { "name" -> "MathWorld", "word" -> "sin", "desc" -> "referring to a definition", "input" -> "*MC.%7E-_*MathWorld-"}}}}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{113., {12., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)/\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "gamma function", WolframAlphaClient`Private`boxes$$ = RowBox[{"Gamma", "[", "x", "]"}], WolframAlphaClient`Private`allassumptions$$ = {{ "type" -> "MultiClash", "word" -> "", "count" -> "4", "Values" -> {{ "name" -> "Function", "word" -> "the input", "desc" -> "a math function", "input" -> "*MC.%7E-_*Function-"}, { "name" -> "MathWorld", "word" -> "the input", "desc" -> "referring to a definition", "input" -> "*MC.%7E-_*MathWorld-"}, { "name" -> "ExamplePage", "word" -> "the input", "desc" -> "a general topic", "input" -> "*MC.%7E-_*ExamplePage-"}, { "name" -> "DistributionNoFluff", "word" -> "gamma", "desc" -> "a probability distribution", "input" -> "*MC.%7E-_*DistributionNoFluff-"}}}}, WolframAlphaClient`Private`assumptions$$ = { "*MC.%7E-_*Function-"}, WolframAlphaClient`Private`open$$ = { 1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{142., {12., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)}, {x, 0, 10}, Filling -> Axis]
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In[2]:=
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Plot[\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "integrate sin(e^x) from 0 to T", WolframAlphaClient`Private`boxes$$ = RowBox[{"Integrate", "[", RowBox[{ RowBox[{"Sin", "[", RowBox[{"E", "^", "x"}], "]"}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "T"}], "}"}]}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{211., {11., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\), {T, 1, 5}, Filling -> 0.625]
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"Gamma"], ScriptLevel -> 0, StripOnInput -> False], StyleBox["\"order\"", LinebreakAdjustments -> {1, 100, 1, 0, 100}, LineIndent -> 0, GrayLevel[0.6], StripOnInput -> False], SuperscriptBox["x", "1"]}}, GridBoxBackground -> {"Columns" -> { GrayLevel[0.949], None, None, None}, "Rows" -> {{None}}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, ColumnsEqual -> False, RowsEqual -> False, GridBoxDividers -> {"Columns" -> { GrayLevel[0.84], GrayLevel[0.84], GrayLevel[0.84], GrayLevel[0.84], GrayLevel[0.84]}, "Rows" -> {{ GrayLevel[0.84]}}, "RowsIndexed" -> { 1 -> GrayLevel[0.84], -1 -> GrayLevel[0.84]}}, GridBoxSpacings -> { "Columns" -> {2, 2, 2, 2, 2}, "Rows" -> {{1}}}, GridBoxAlignment -> { "Columns" -> {{Left}}, "Rows" -> {{Baseline}}}, AllowScriptLevelChange -> False], TagBoxWrapper["Separator" -> " | "]], LineSpacing -> {1, 0, 1.5}, LineIndent -> 0]}}, GridBoxItemSize -> { "Columns" -> {{Automatic}}, "Rows" -> {{Automatic}}}, ColumnsEqual -> False, RowsEqual -> False, GridBoxSpacings -> {"Columns" -> {{ AbsoluteThickness[-1]}}, "Rows" -> {{0}}}, AllowScriptLevelChange -> False], TagBoxWrapper["Separator" -> " | "]], PolynomialForm[#, TraditionalOrder -> False]& ], TraditionalForm]], "Output"]}], XMLElement["dataformats", {}, {}]}], XMLElement["infos", {"count" -> "1"}, { XMLElement[ "info", { "text" -> "\[CapitalGamma](x) is the gamma function"}, { XMLElement[ "link", { "url" -> "https://reference.wolfram.com/mathematica/ref/\ Gamma.html", "text" -> "Documentation", "title" -> "Mathematica"}, {}], XMLElement[ "link", { "url" -> "https://functions.wolfram.com/GammaBetaErf/Gamma", "text" -> "Properties", "title" -> "Wolfram Functions Site"}, {}], XMLElement[ "link", { "url" -> "https://mathworld.wolfram.com/GammaFunction.html", "text" -> "Definition", "title" -> "MathWorld"}, {}]}]}]}], pod2$$ = XMLElement[ "pod", {"title" -> "Series expansion at x=0", "scanner" -> "Series", "id" -> "SeriesExpansionAtX = 0", "position" -> "200", "error" -> "false", "numsubpods" -> "1"}, { XMLElement["subpod", {"title" -> ""}, { XMLElement["minput", {}, {"Series[Gamma[x], {x, 0, 1}]"}], XMLElement[ "moutput", {}, { "SeriesData[x, 0, {1, -EulerGamma, (6 EulerGamma^2 + \ Pi^2)/12}, -1, 2, 1]"}], XMLElement["cell", {"compressed" -> False, "string" -> True}, { Cell[ BoxData[ FormBox[ InterpretationBox[ RowBox[{ FractionBox["1", "x"], "-", TagBox["\[DoubledGamma]", Function[{}, EulerGamma]], "+", RowBox[{ FractionBox["1", "12"], " ", RowBox[{"(", RowBox[{ RowBox[{"6", " ", SuperscriptBox[ TagBox["\[DoubledGamma]", Function[{}, EulerGamma]], "2"]}], "+", SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", "x"}], "+", InterpretationBox[ RowBox[{ StyleBox["O", FontFamily -> "Bitstream Vera Sans", FontSize -> -1 + Inherited], "(", SuperscriptBox["x", "2"], ")"}], SeriesData[x, 0, {}, -1, 2, 1], Editable -> False]}], SeriesData[ x, 0, {1, -EulerGamma, Rational[1, 12] (6 EulerGamma^2 + Pi^2)}, -1, 2, 1], Editable -> False], TraditionalForm]], "Output"]}], XMLElement["dataformats", {}, {}]}], XMLElement["states", {"count" -> "1"}, { XMLElement[ "state", { "name" -> "More terms", "input" -> "Series expansion at x=0_More terms"}, {}]}], XMLElement["infos", {"count" -> "1"}, { XMLElement[ "info", { "text" -> "\[Gamma] is the Euler-Mascheroni constant"}, { XMLElement[ "link", { "url" -> "https://reference.wolfram.com/mathematica/ref/\ EulerGamma.html", "text" -> "Documentation", "title" -> "Documentation"}, {}], XMLElement[ "link", { "url" -> "https://mathworld.wolfram.com/Euler-\ MascheroniConstant.html", "text" -> "Definition", "title" -> "MathWorld"}, {}]}]}]}], pod3$$ = XMLElement[ "pod", {"title" -> "Approximations about x = 0 up to order 3", "scanner" -> "Series", "id" -> "PlotOfSeriesExpansionAtX = 0", "position" -> "300", "error" -> "false", "numsubpods" -> "1"}, { XMLElement["subpod", {"title" -> ""}, { XMLElement["cell", {"compressed" -> True, "string" -> False}, { Cell[ BoxData[ FormBox[ TagBox[ GridBox[{{ 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\!\(\* NamespaceBox["LinguisticAssistant", DynamicModuleBox[{WolframAlphaClient`Private`query$$ = "integrate sin(10x) e^-x^2 from 0 to T", WolframAlphaClient`Private`boxes$$ = RowBox[{"Integrate", "[", RowBox[{ RowBox[{ RowBox[{"Sin", "[", RowBox[{"10", "*", "x"}], "]"}], "/", RowBox[{"E", "^", RowBox[{"x", "^", "2"}]}]}], ",", " ", RowBox[{"{", RowBox[{"x", ",", " ", "0", ",", " ", "T"}], "}"}]}], "]"}], WolframAlphaClient`Private`allassumptions$$ = {}, WolframAlphaClient`Private`assumptions$$ = {}, WolframAlphaClient`Private`open$$ = {1}}, DynamicBox[ToBoxes[ AlphaIntegration`LinguisticAssistantBoxes["", 1, Dynamic[WolframAlphaClient`Private`query$$], Dynamic[WolframAlphaClient`Private`boxes$$], Dynamic[WolframAlphaClient`Private`allassumptions$$], Dynamic[WolframAlphaClient`Private`assumptions$$], Dynamic[WolframAlphaClient`Private`open$$]], StandardForm], ImageSizeCache->{257., {11., 17.}}], DynamicModuleValues:>{}], BaseStyle->{Deployed -> True}, DeleteWithContents->True, Editable->False, SelectWithContents->True]\)
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\!\(\* NamespaceBox["WolframAlphaQueryParseResults", DynamicModuleBox[{Typeset`q$$ = "derivative x/(x^2-ln sin x)", Typeset`newq$$ = "derivative x/(x^2-ln sin x)", Typeset`chosen$$ = "D[x/(x^2 - Log[Sin[x]]), x]"}, PaneSelectorBox[{False-> DynamicModuleBox[{WolframAlphaClient`Private`show$$ = False}, TagBox[ FrameBox[ TagBox[GridBox[{ { InputFieldBox[Dynamic[Typeset`newq$$], String, Appearance->None, BaseStyle->{"CalculateInput"}, ContinuousAction->True, Enabled->True, FieldSize->{{1, 40}, {1, DirectedInfinity[1]}}], ItemBox[ ButtonBox[ PaneSelectorBox[{True-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "OrangeSquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ], False-> TagBox[ TooltipBox[ DynamicBox[FEPrivate`FrontEndResource["WABitmaps", "GraySquarePlus"], ImageSizeCache->{10., {3., 8.}}], DynamicBox[ ToBoxes[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"], StandardForm]]], Annotation[#, Dynamic[ FEPrivate`FrontEndResource["WAStrings", "ShowAllResults"]], "Tooltip"]& ]}, Dynamic[ WolframAlphaClient`Private`show$$], ImageSize->All], Appearance->None, ButtonFunction:>If[ Or[ CurrentValue["OptionKey"], CurrentValue["AltKey"]], SelectionMove[ ButtonNotebook[], All, ButtonCell, AutoScroll -> False]; 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To get detailed information on your query, use double equal signs.
In[7]:=
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y''=-y+0.1sin(5y)-0.2y'