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http://functions.wolfram.com/03.06.21.0087.01
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Integrate[1/(AiryAi[z]^2 + AiryBi[z]^2), z] == Pi ArcTan[AiryBi[z]/AiryAi[z]]
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["AiryAi", "[", "z", "]"]], "2"], " ", "+", SuperscriptBox[RowBox[List["AiryBi", "[", "z", "]"]], "2"]]]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List["\[Pi]", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["AiryBi", "[", "z", "]"]], RowBox[List["AiryAi", "[", "z", "]"]]], "]"]]]]]]]]
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<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mo> ∫ </mo> <mrow> <mfrac> <mn> 1 </mn> <mrow> <msup> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mi> π </mi> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> AiryBi </ci> <ci> z </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <arctan /> <apply> <times /> <apply> <ci> AiryBi </ci> <ci> z </ci> </apply> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["\[Integral]", RowBox[List[FractionBox["1", RowBox[List[SuperscriptBox[RowBox[List["AiryAi", "[", "z_", "]"]], "2"], "+", SuperscriptBox[RowBox[List["AiryBi", "[", "z_", "]"]], "2"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["\[Pi]", " ", RowBox[List["ArcTan", "[", FractionBox[RowBox[List["AiryBi", "[", "z", "]"]], RowBox[List["AiryAi", "[", "z", "]"]]], "]"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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