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http://functions.wolfram.com/06.40.21.0049.01
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Integrate[CoshIntegral[a z] CoshIntegral[b z], z] ==
(1/(2 a b)) (2 a b z CoshIntegral[a z] CoshIntegral[b z] -
2 b CoshIntegral[b z] Sinh[a z] - 2 a CoshIntegral[a z] Sinh[b z] -
a SinhIntegral[(a - b) z] + b SinhIntegral[(a - b) z] +
a SinhIntegral[(a + b) z] + b SinhIntegral[(a + b) z])
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", " ", "a", " ", "b"]]], RowBox[List["(", RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", "z", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", 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> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Chi </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> <mfrac> <mn> 1 </mn> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> b </mi> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> <mo> ⁢ </mo> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> Chi </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> sinh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> Shi </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> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> Shi </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> <mo> + </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <mrow> <mi> Shi </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> <mo> + </mo> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mrow> <mi> Shi </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 /> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <ci> b </ci> <ci> z </ci> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> b </ci> <apply> <sinh /> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> a </ci> <apply> <ci> CoshIntegral </ci> <apply> <times /> <ci> a </ci> <ci> z </ci> </apply> </apply> <apply> <sinh /> <apply> <times /> <ci> b </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <ci> SinhIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <ci> SinhIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> b </ci> </apply> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <ci> SinhIntegral </ci> <apply> <times /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <ci> z </ci> </apply> </apply> </apply> <apply> <times /> <ci> b </ci> <apply> <ci> SinhIntegral </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[RowBox[List["CoshIntegral", "[", RowBox[List["a_", " ", "z_"]], "]"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["b_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["2", " ", "a", " ", "b", " ", "z", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "b", " ", RowBox[List["CoshIntegral", "[", RowBox[List["b", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["a", " ", "z"]], "]"]]]], "-", RowBox[List["2", " ", "a", " ", RowBox[List["CoshIntegral", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["Sinh", "[", RowBox[List["b", " ", "z"]], "]"]]]], "-", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "-", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["a", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["SinhIntegral", "[", RowBox[List[RowBox[List["(", RowBox[List["a", "+", "b"]], ")"]], " ", "z"]], "]"]]]]]], RowBox[List["2", " ", "a", " ", "b"]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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){kind=small}
