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http://functions.wolfram.com/01.20.21.0319.01
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Integrate[z E^(c z + e) Cosh[c z], z] ==
(E^e (2 c^2 z^2 + E^(2 c z) (-1 + 2 c z)))/(8 c^2)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List["z", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c", " ", "z"]], "+", "e"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", "z"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]]]], ")"]]]], RowBox[List["8", " ", SuperscriptBox["c", "2"]]]]]]]]
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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> <msup> <mi> ⅇ </mi> <mrow> <mi> e </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </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> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mi> e </mi> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 8 </mn> <mo> ⁢ </mo> <msup> <mi> c </mi> <mn> 2 </mn> </msup> </mrow> </mfrac> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <times /> <ci> z </ci> <apply> <power /> <exponentiale /> <apply> <plus /> <ci> e </ci> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> <apply> <cosh /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <ci> e </ci> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 8 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> <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["\[Integral]", RowBox[List[RowBox[List["z_", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["c_", " ", "z_"]], "+", "e_"]]], " ", RowBox[List["Cosh", "[", RowBox[List["c_", " ", "z_"]], "]"]]]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", "e"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["z", "2"]]], "+", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c", " ", "z"]]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", RowBox[List["2", " ", "c", " ", "z"]]]], ")"]]]]]], ")"]]]], RowBox[List["8", " ", SuperscriptBox["c", "2"]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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