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 | | http://functions.wolfram.com/06.35.21.0065.01 | 
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 | | Integrate[z ExpIntegralEi[a z] ExpIntegralEi[b z], z] == 
 (-(1/(2 a^2 b^2))) ((-a) b E^((a + b) z) + b^2 E^(a z) (-1 + a z) 
    ExpIntegralEi[b z] + a^2 ExpIntegralEi[a z] (E^(b z) (-1 + b z) - 
     b^2 z^2 ExpIntegralEi[b z]) + (a^2 + b^2) ExpIntegralEi[(a + b) z]) | 
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 | | Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]]]]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", "z"]]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "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>  <mrow>  <mi> z </mi>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ⅆ </mo>  <mi> z </mi>  </mrow>  </mrow>  </mrow>  <mo> ⩵ </mo>  <mrow>  <mrow>  <mo> - </mo>  <mfrac>  <mn> 1 </mn>  <mrow>  <mn> 2 </mn>  <mo> ⁢ </mo>  <msup>  <mi> a </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  </mrow>  </mfrac>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> - </mo>  <mrow>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> z </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <msup>  <mi> a </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> - </mo>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> b </mi>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> b </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  </mrow>  <mo> + </mo>  <mrow>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  <mo> ⁢ </mo>  <msup>  <mi> ⅇ </mi>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  </msup>  <mo> ⁢ </mo>  <mrow>  <mo> ( </mo>  <mrow>  <mrow>  <mi> a </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> - </mo>  <mn> 1 </mn>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mi> b </mi>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  <mo> + </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <msup>  <mi> a </mi>  <mn> 2 </mn>  </msup>  <mo> + </mo>  <msup>  <mi> b </mi>  <mn> 2 </mn>  </msup>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mrow>  <mi> Ei </mi>  <mo> ⁡ </mo>  <mo> ( </mo>  <mrow>  <mrow>  <mo> ( </mo>  <mrow>  <mi> a </mi>  <mo> + </mo>  <mi> b </mi>  </mrow>  <mo> ) </mo>  </mrow>  <mo> ⁢ </mo>  <mi> z </mi>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <mo> ) </mo>  </mrow>  </mrow>  </mrow>  <annotation-xml encoding='MathML-Content'>  <apply>  <eq />  <apply>  <int />  <bvar>  <ci> z </ci>  </bvar>  <apply>  <times />  <ci> z </ci>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <ci> a </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <cn type='integer'> 1 </cn>  <apply>  <power />  <apply>  <times />  <cn type='integer'> 2 </cn>  <apply>  <power />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <ci> a </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <apply>  <power />  <exponentiale />  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> z </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  </apply>  <apply>  <power />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <times />  <cn type='integer'> -1 </cn>  <apply>  <times />  <ci> a </ci>  <ci> b </ci>  <apply>  <power />  <exponentiale />  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <ci> b </ci>  </apply>  <ci> z </ci>  </apply>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <exponentiale />  <apply>  <times />  <ci> a </ci>  <ci> z </ci>  </apply>  </apply>  <apply>  <plus />  <apply>  <times />  <ci> a </ci>  <ci> z </ci>  </apply>  <cn type='integer'> -1 </cn>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <ci> b </ci>  <ci> z </ci>  </apply>  </apply>  </apply>  <apply>  <times />  <apply>  <plus />  <apply>  <power />  <ci> a </ci>  <cn type='integer'> 2 </cn>  </apply>  <apply>  <power />  <ci> b </ci>  <cn type='integer'> 2 </cn>  </apply>  </apply>  <apply>  <ci> ExpIntegralEi </ci>  <apply>  <times />  <apply>  <plus />  <ci> a </ci>  <ci> b </ci>  </apply>  <ci> z </ci>  </apply>  </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[RowBox[List["z_", " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", "a"]], " ", "b", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]]]]], "+", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["\[ExponentialE]", RowBox[List["a", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["a", " ", "z"]]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["b", " ", "z"]]]], ")"]]]], "-", RowBox[List[SuperscriptBox["b", "2"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List["b", " ", "z"]], "]"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["a", "2"], "+", SuperscriptBox["b", "2"]]], ")"]], " ", RowBox[List["ExpIntegralEi", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List["2", " ", SuperscriptBox["a", "2"], " ", SuperscriptBox["b", "2"]]]]]]]]]] | 
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 | | Date Added to functions.wolfram.com (modification date) | 
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