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http://functions.wolfram.com/01.20.21.0412.01
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Integrate[Cosh[a z^r + c], z] ==
(-(1/(2 r))) ((z (E^(2 c) ExpIntegralE[(-1 + r)/r, (-a) z^r] +
ExpIntegralE[(-1 + r)/r, a z^r]))/E^c)
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Cell[BoxData[RowBox[List[RowBox[List["\[Integral]", RowBox[List[RowBox[List["Cosh", "[", RowBox[List[RowBox[List["a", " ", SuperscriptBox["z", "r"]]], "+", "c"]], "]"]], RowBox[List["\[DifferentialD]", "z"]]]]]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["2", " ", "r"]]]]], RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "c"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c"]]], " ", RowBox[List["ExpIntegralE", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "r"]], "r"], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List["ExpIntegralE", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "r"]], "r"], ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], ")"]]]], ")"]]]]]]]]
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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> cosh </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> + </mo> <mi> c </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mo> - </mo> <mi> c </mi> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> <mtext> </mtext> </mrow> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> r </mi> </mrow> </mfrac> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> c </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox["E", ExpIntegralE] </annotation> </semantics> <mfrac> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> r </mi> </mfrac> </msub> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mi> a </mi> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msub> <semantics> <mi> E </mi> <annotation encoding='Mathematica'> TagBox["E", ExpIntegralE] </annotation> </semantics> <mfrac> <mrow> <mi> r </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mi> r </mi> </mfrac> </msub> <mo> ( </mo> <mrow> <mi> a </mi> <mo> ⁢ </mo> <msup> <mi> z </mi> <mi> r </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <int /> <bvar> <ci> z </ci> </bvar> <apply> <cosh /> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> <ci> c </ci> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> r </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> <apply> <power /> <ci> z </ci> <ci> r </ci> </apply> </apply> </apply> </apply> <apply> <ci> ExpIntegralE </ci> <apply> <times /> <apply> <plus /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> <apply> <power /> <ci> r </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <power /> <ci> z </ci> <ci> r </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["Cosh", "[", RowBox[List[RowBox[List["a_", " ", SuperscriptBox["z_", "r_"]]], "+", "c_"]], "]"]], RowBox[List["\[DifferentialD]", "z_"]]]]]], "]"]], "\[RuleDelayed]", RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "c"]]], " ", "z", " ", RowBox[List["(", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["2", " ", "c"]]], " ", RowBox[List["ExpIntegralE", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "r"]], "r"], ",", RowBox[List[RowBox[List["-", "a"]], " ", SuperscriptBox["z", "r"]]]]], "]"]]]], "+", RowBox[List["ExpIntegralE", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", "1"]], "+", "r"]], "r"], ",", RowBox[List["a", " ", SuperscriptBox["z", "r"]]]]], "]"]]]], ")"]]]], RowBox[List["2", " ", "r"]]]]]]]]] |
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Date Added to functions.wolfram.com (modification date)
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