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http://functions.wolfram.com/01.03.21.0444.01
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Integrate[(E^z + E^(5 z))/(-1 + E^z - E^(2 z) + E^(3 z)), z] ==
(1/2) (2 E^z + E^(2 z) - (1 + I) ArcTan[(-1 + E^z)/(1 + E^z)] +
(1 - I) ArcTan[(1 + E^z)/(-1 + E^z)] + 2 Log[-1 + E^z] - Log[1 + E^(2 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> <mfrac> <mrow> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 5 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> <mo> - </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 3 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> </mrow> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ⅆ </mo> <mi> z </mi> </mrow> </mrow> </mrow> <mo> ⩵ </mo> <mrow> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> + </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <msup> <mi> tan </mi> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> </msup> <mo> ( </mo> <mfrac> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <msup> <mi> ⅇ </mi> <mi> z </mi> </msup> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> - </mo> <mrow> <mi> log </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> </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> <times /> <apply> <plus /> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 5 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> z </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='complex-cartesian'> -1 <sep /> -1 </cn> <apply> <arctan /> <apply> <times /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <apply> <arctan /> <apply> <times /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ln /> <apply> <plus /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ln /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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