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 Coth

 http://functions.wolfram.com/01.22.21.0203.01

 Input Form

 Integrate[E^(p z) Cos[a z] Sinh[b z] Coth[c z], z] == (1/4) ((E^(((-I) a - b + p) z) Hypergeometric2F1[((-I) a - b + p)/(2 c), 1, ((-I) a - b + 2 c + p)/(2 c), E^(2 c z)])/((-I) a - b + p) + (E^((I a - b + p) z) Hypergeometric2F1[(I a - b + p)/(2 c), 1, (I a - b + 2 c + p)/(2 c), E^(2 c z)])/(I a - b + p) - (E^(((-I) a + b + p) z) Hypergeometric2F1[((-I) a + b + p)/(2 c), 1, ((-I) a + b + 2 c + p)/(2 c), E^(2 c z)])/((-I) a + b + p) - (E^((I a + b + p) z) Hypergeometric2F1[(I a + b + p)/(2 c), 1, (I a + b + 2 c + p)/(2 c), E^(2 c z)])/(I a + b + p) + (1/((-I) a - b + 2 c + p)) (E^(((-I) a - b + 2 c + p) z) Hypergeometric2F1[((-I) a - b + 2 c + p)/(2 c), 1, ((-I) a - b + 4 c + p)/(2 c), E^(2 c z)]) + (E^((I a - b + 2 c + p) z) Hypergeometric2F1[(I a - b + 2 c + p)/(2 c), 1, (I a - b + 4 c + p)/(2 c), E^(2 c z)])/(I a - b + 2 c + p) - (1/((-I) a + b + 2 c + p)) (E^(((-I) a + b + 2 c + p) z) Hypergeometric2F1[((-I) a + b + 2 c + p)/(2 c), 1, ((-I) a + b + 4 c + p)/(2 c), E^(2 c z)]) - (E^((I a + b + 2 c + p) z) Hypergeometric2F1[(I a + b + 2 c + p)/(2 c), 1, (I a + b + 4 c + p)/(2 c), E^(2 c z)])/(I a + b + 2 c + p))

 Standard Form

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 MathML Form

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18