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http://functions.wolfram.com/01.20.21.4887.01
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Integrate[(E^(p z) Cos[e z] Sinh[d z])/(a + b Cosh[c z])^2, z] ==
(1/4) (-((E^((c - d - I e + p) z) (a (a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c - d - I e + p)/c, 1, 2 + (-d - I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c - d - I e + p)/c, 1, 2 + (-d - I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))] + (-a^2 + b^2)
(Hypergeometric2F1[(c - d - I e + p)/c, 2, 2 + (-d - I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] - Hypergeometric2F1[
(c - d - I e + p)/c, 2, 2 + (-d - I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2]
(Hypergeometric2F1[(c - d - I e + p)/c, 2, 2 + (-d - I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[
(c - d - I e + p)/c, 2, 2 + (-d - I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/(b (a^2 - b^2)^(3/2)
(c - d - I e + p))) + (E^((c + d - I e + p) z)
(a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d - I e + p)/c, 1,
2 + (d - I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] +
a (-a + Sqrt[a^2 - b^2]) Hypergeometric2F1[(c + d - I e + p)/c, 1,
2 + (d - I e + p)/c, -((b E^(c z))/(a + Sqrt[a^2 - b^2]))] +
(-a^2 + b^2) (Hypergeometric2F1[(c + d - I e + p)/c, 2,
2 + (d - I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] -
Hypergeometric2F1[(c + d - I e + p)/c, 2, 2 + (d - I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2]
(Hypergeometric2F1[(c + d - I e + p)/c, 2, 2 + (d - I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[
(c + d - I e + p)/c, 2, 2 + (d - I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/
(b (a^2 - b^2)^(3/2) (c + d - I e + p)) -
(E^((c - d + I e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[
(c - d + I e + p)/c, 1, 2 + (-d + I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c - d + I e + p)/c, 1, 2 + (-d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))] +
(-a^2 + b^2) (Hypergeometric2F1[(c - d + I e + p)/c, 2,
2 + (-d + I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] -
Hypergeometric2F1[(c - d + I e + p)/c, 2, 2 + (-d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2]
(Hypergeometric2F1[(c - d + I e + p)/c, 2, 2 + (-d + I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[
(c - d + I e + p)/c, 2, 2 + (-d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/
(b (a^2 - b^2)^(3/2) (c - d + I e + p)) +
(E^((c + d + I e + p) z) (a (a + Sqrt[a^2 - b^2]) Hypergeometric2F1[
(c + d + I e + p)/c, 1, 2 + (d + I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + a (-a + Sqrt[a^2 - b^2])
Hypergeometric2F1[(c + d + I e + p)/c, 1, 2 + (d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))] +
(-a^2 + b^2) (Hypergeometric2F1[(c + d + I e + p)/c, 2,
2 + (d + I e + p)/c, (b E^(c z))/(-a + Sqrt[a^2 - b^2])] -
Hypergeometric2F1[(c + d + I e + p)/c, 2, 2 + (d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))]) - a Sqrt[a^2 - b^2]
(Hypergeometric2F1[(c + d + I e + p)/c, 2, 2 + (d + I e + p)/c,
(b E^(c z))/(-a + Sqrt[a^2 - b^2])] + Hypergeometric2F1[
(c + d + I e + p)/c, 2, 2 + (d + I e + p)/c,
-((b E^(c z))/(a + Sqrt[a^2 - b^2]))])))/
(b (a^2 - b^2)^(3/2) (c + d + I e + p)))
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<ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <ci> d </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 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type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <ci> 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2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <ci> a </ci> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 1 </cn> <apply> <plus /> <apply> 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<cn type='integer'> -1 </cn> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <plus /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </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> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </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> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <ci> b </ci> <apply> <power /> <exponentiale /> <apply> <times /> <ci> c </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <plus /> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> a </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> <ci> p </ci> </apply> <apply> <power /> <ci> c </ci> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> 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type='rational'> 3 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> d </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <ci> e </ci> </apply> </apply> <ci> p </ci> </apply> <ci> z </ci> </apply> </apply> <apply> <plus /> <apply> <times /> <ci> a </ci> <apply> <plus /> <ci> a </ci> <apply> <power /> <apply> <plus /> <apply> <power /> <ci> a </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <cn type='rational'> 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Date Added to functions.wolfram.com (modification date)
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