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http://functions.wolfram.com/01.20.21.1347.01
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Integrate[E^(b z) Csc[c z] Cosh[c z], z] ==
-(I ((b + (1 + I) c) E^((b - (1 - I) c) z) Hypergeometric2F1[
-((I (b - (1 - I) c))/(2 c)), 1, -((I (b - (1 - 3 I) c))/(2 c)),
E^(2 I c z)] + (b - (1 - I) c) E^((b + (1 + I) c) z)
Hypergeometric2F1[-((I (b + (1 + I) c))/(2 c)), 1,
-((I (b + (1 + 3 I) c))/(2 c)), E^(2 I c z)]))/
((b - (1 - I) c) (b + (1 + I) c))
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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> <msup> <mi> ⅇ </mi> <mrow> <mi> b </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> </msup> <mo> ⁢ </mo> <mrow> <mi> csc </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <mi> c </mi> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <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> <mrow> <mrow> <mo> - </mo> <mfrac> <mn> 1 </mn> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> - </mo> <mrow> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> ⅈ </mi> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mi> c </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mrow> <mi> c </mi> <mo> ⁢ 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/> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <imaginaryi /> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='complex-cartesian'> 1 <sep /> -1 </cn> <ci> c </ci> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <cn type='complex-cartesian'> 1 <sep /> 3 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <ci> c </ci> <apply> <plus /> <cn type='integer'> 1 </cn> <imaginaryi /> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> 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type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> <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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