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http://functions.wolfram.com/01.20.21.4765.01
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Integrate[Sin[d z]/(a + b Sinh[e z] + c Cosh[e z])^2, z] ==
(-(1/2)) I
(-((E^(((-I) d + e) z) ((-a) (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 (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^2 Hypergeometric2F1[((-I) d + e)/e, 2, 2 - (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
b^2 Hypergeometric2F1[((-I) d + e)/e, 2, 2 - (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
c^2 Hypergeometric2F1[((-I) d + e)/e, 2, 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, 2,
2 - (I d)/e, ((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
a^2 Hypergeometric2F1[((-I) d + e)/e, 2, 2 - (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] -
b^2 Hypergeometric2F1[((-I) d + e)/e, 2, 2 - (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
c^2 Hypergeometric2F1[((-I) d + e)/e, 2, 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, 2,
2 - (I d)/e, -(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) (a^2 + b^2 - c^2)^(3/2) ((-I) d + e))) +
(E^((I d + e) z) ((-a) (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 (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^2 Hypergeometric2F1[(I d + e)/e, 2, 2 + (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] +
b^2 Hypergeometric2F1[(I d + e)/e, 2, 2 + (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
c^2 Hypergeometric2F1[(I d + e)/e, 2, 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, 2, 2 + (I d)/e,
((b + c) E^(e z))/(-a + Sqrt[a^2 + b^2 - c^2])] -
a^2 Hypergeometric2F1[(I d + e)/e, 2, 2 + (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] -
b^2 Hypergeometric2F1[(I d + e)/e, 2, 2 + (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))] +
c^2 Hypergeometric2F1[(I d + e)/e, 2, 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, 2, 2 + (I d)/e,
-(((b + c) E^(e z))/(a + Sqrt[a^2 + b^2 - c^2]))]))/
((b - c) (a^2 + b^2 - c^2)^(3/2) (I d + e)))
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</apply> </apply> </annotation-xml> </semantics> </math>
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Date Added to functions.wolfram.com (modification date)
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