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http://functions.wolfram.com/01.23.21.0207.01
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Integrate[Sin[a z] Cosh[b z] Csch[c z], z] ==
(I E^(b z) (E^((-b) z) + E^(b z)) (1 - E^(2 c z))
((E^(((-I) a - b + c) z) Hypergeometric2F1[1, -((I a + b - c)/(2 c)),
-((I a + b - 3 c)/(2 c)), E^(2 c z)])/((-I) a - b + c) +
(E^((I a - b + c) z) Hypergeometric2F1[1, (I a - b + c)/(2 c),
(I a - b + 3 c)/(2 c), E^(2 c z)])/((-I) a + b - c) +
I ((1/(a + I (b + c))) (E^(((-I) a + b + c) z) Hypergeometric2F1[1,
((-I) a + b + c)/(2 c), ((-I) a + b + 3 c)/(2 c), E^(2 c z)]) +
(1/(a - I (b + c))) (E^((I a + b + c) z) Hypergeometric2F1[1,
(I a + b + c)/(2 c), (I a + b + 3 c)/(2 c), E^(2 c z)]))))/
(2 (1 + E^(2 b z)) (-1 + E^(2 c z)))
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