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http://functions.wolfram.com/01.20.21.4778.01
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Integrate[Cos[d z]/(a + b Sinh[e z] + c Cosh[e z]), z] ==
(1/2) (-((E^(((-I) d + e) z) ((a + Sqrt[a^2 + b^2 - c^2])
Hypergeometric2F1[((-I) d + e)/e, 1, 2 - (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
(-a + Sqrt[a^2 + b^2 - c^2]) Hypergeometric2F1[((-I) d + e)/e, 1,
2 - (I d)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) Sqrt[a^2 + b^2 - c^2] ((-I) d + e))) -
(E^((I d + e) z) ((a + Sqrt[a^2 + b^2 - c^2]) Hypergeometric2F1[
(I d + e)/e, 1, 2 + (I d)/e, ((b + c) E^(e z))/
(-a + Sqrt[a^2 + b^2 - c^2])] + (-a + Sqrt[a^2 + b^2 - c^2])
Hypergeometric2F1[(I d + e)/e, 1, 2 + (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) Sqrt[a^2 + b^2 - c^2] (I d + e)))
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<apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> e </ci> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <cn type='integer'> 2 </cn> <apply> <times /> <imaginaryi /> <ci> d </ci> <apply> <power /> <ci> e </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <plus /> <ci> b </ci> <ci> c </ci> </apply> <apply> <power /> <exponentiale /> <apply> <times /> <ci> e </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <plus /> <ci> b </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> e </ci> <apply> <times /> <imaginaryi /> <ci> d </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>
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