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http://functions.wolfram.com/01.20.21.3876.01
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Integrate[(E^(p z) Cosh[e z] Cosh[d z])/(a + b Cos[c z]^2), z] ==
(1/4) (-((E^((2 I c - d - e + p) z) ((-2 a - b - 2 Sqrt[a] Sqrt[a + b])
Hypergeometric2F1[1 - (I (-d - e + p))/(2 c), 1,
2 - (I (-d - e + p))/(2 c), -((b E^(2 I c z))/
(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] +
(2 a + b - 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
1 - (I (-d - e + p))/(2 c), 1, 2 - (I (-d - e + p))/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))]))/
(Sqrt[a] b Sqrt[a + b] (2 I c - d - e + p))) -
(E^((2 I c + d - e + p) z) ((-2 a - b - 2 Sqrt[a] Sqrt[a + b])
Hypergeometric2F1[1 - (I (d - e + p))/(2 c), 1,
2 - (I (d - e + p))/(2 c), -((b E^(2 I c z))/(2 a + b -
2 Sqrt[a] Sqrt[a + b]))] + (2 a + b - 2 Sqrt[a] Sqrt[a + b])
Hypergeometric2F1[1 - (I (d - e + p))/(2 c), 1,
2 - (I (d - e + p))/(2 c), -((b E^(2 I c z))/(2 a + b +
2 Sqrt[a] Sqrt[a + b]))]))/(Sqrt[a] b Sqrt[a + b]
(2 I c + d - e + p)) - (E^((2 I c - d + e + p) z)
((-2 a - b - 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
1 - (I (-d + e + p))/(2 c), 1, 2 - (I (-d + e + p))/(2 c),
-((b E^(2 I c z))/(2 a + b - 2 Sqrt[a] Sqrt[a + b]))] +
(2 a + b - 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[
1 - (I (-d + e + p))/(2 c), 1, 2 - (I (-d + e + p))/(2 c),
-((b E^(2 I c z))/(2 a + b + 2 Sqrt[a] Sqrt[a + b]))]))/
(Sqrt[a] b Sqrt[a + b] (2 I c - d + e + p)) -
(E^((2 I c + d + e + p) z) ((-2 a - b - 2 Sqrt[a] Sqrt[a + b])
Hypergeometric2F1[1 - (I (d + e + p))/(2 c), 1,
2 - (I (d + e + p))/(2 c), -((b E^(2 I c z))/(2 a + b -
2 Sqrt[a] Sqrt[a + b]))] + (2 a + b - 2 Sqrt[a] Sqrt[a + b])
Hypergeometric2F1[1 - (I (d + e + p))/(2 c), 1,
2 - (I (d + e + p))/(2 c), -((b E^(2 I c z))/(2 a + b +
2 Sqrt[a] Sqrt[a + b]))]))/(Sqrt[a] b Sqrt[a + b]
(2 I c + d + e + p)))
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<ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <ci> b </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <ci> a </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> b </ci> <apply> <power /> <apply> <plus /> <ci> a </ci> <ci> b </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <ci> d </ci> <ci> e </ci> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> c </ci> </apply> <ci> p </ci> </apply> </apply> <cn type='integer'> -1 </cn> </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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