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http://functions.wolfram.com/03.06.21.0091.01
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Integrate[(AiryAi[x] AiryBi[x])/(AiryAi[x]^2 + AiryBi[x]^2)^2,
{x, 0, Infinity}] == Pi/8
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Cell[BoxData[RowBox[List[RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["AiryAi", "[", "x", "]"]], " ", RowBox[List["AiryBi", "[", "x", "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["AiryAi", "[", "x", "]"]], "2"], "+", SuperscriptBox[RowBox[List["AiryBi", "[", "x", "]"]], "2"]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "x"]]]]]], "\[Equal]", FractionBox["\[Pi]", "8"]]]]]
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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> <msubsup> <mo> ∫ </mo> <mn> 0 </mn> <mi> ∞ </mi> </msubsup> <mrow> <mfrac> <mrow> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <msup> <mrow> <mi> Ai </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> <mo> + </mo> <msup> <mrow> <mi> Bi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mi> x </mi> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> x </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mfrac> <mi> π </mi> <mn> 8 </mn> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> x </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <ci> AiryAi </ci> <ci> x </ci> </apply> <apply> <ci> AiryBi </ci> <ci> x </ci> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <ci> AiryAi </ci> <ci> x </ci> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <ci> AiryBi </ci> <ci> x </ci> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <pi /> <apply> <power /> <cn type='integer'> 8 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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| Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubsuperscriptBox["\[Integral]", "0", "\[Infinity]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["AiryAi", "[", "x_", "]"]], " ", RowBox[List["AiryBi", "[", "x_", "]"]]]], SuperscriptBox[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["AiryAi", "[", "x_", "]"]], "2"], "+", SuperscriptBox[RowBox[List["AiryBi", "[", "x_", "]"]], "2"]]], ")"]], "2"]], RowBox[List["\[DifferentialD]", "x_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox["\[Pi]", "8"]]]]] |
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Date Added to functions.wolfram.com (modification date)
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