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 Cosh

 http://functions.wolfram.com/01.20.21.1312.01

 Input Form

 Integrate[E^(p z) (a + b E^(d z))^\[Beta] Cos[e z]^m Cosh[c z], z] == (1/((c - p) (c + p))) ((2^(-1 - m) (a + b E^(d z))^\[Beta] Binomial[m, m/2] ((-E^((-c + p) z)) (c + p) Hypergeometric2F1[(-c + p)/d, -\[Beta], (-c + d + p)/d, -((b E^(d z))/a)] + E^((c + p) z) (c - p) Hypergeometric2F1[(c + p)/d, -\[Beta], (c + d + p)/d, -((b E^(d z))/a)]) (1 - Mod[m, 2]))/(1 + (b E^(d z))/a)^\[Beta]) + (2^(-1 - m) (a + b E^(d z))^\[Beta] Sum[Binomial[m, k] (((-E^((c - I e (2 k - m) + p) z)) (-c + I e (2 k - m) + p) Hypergeometric2F1[(c - I e (2 k - m) + p)/ d, -\[Beta], (c + d - I e (2 k - m) + p)/d, -((b E^(d z))/a)] + E^((-c + I e (2 k - m) + p) z) (-c + I e (2 k - m) - p) Hypergeometric2F1[(-c + I e (2 k - m) + p)/d, -\[Beta], (-c + d + I e (2 k - m) + p)/d, -((b E^(d z))/a)])/ ((-c + I e (2 k - m) - p) (-c + I e (2 k - m) + p)) + ((-E^((-c - I e (2 k - m) + p) z)) (c + I e (2 k - m) + p) Hypergeometric2F1[(-c - I e (2 k - m) + p)/d, -\[Beta], (-c + d - I e (2 k - m) + p)/d, -((b E^(d z))/a)] + E^((c + I e (2 k - m) + p) z) (c + I e (2 k - m) - p) Hypergeometric2F1[(c + I e (2 k - m) + p)/d, -\[Beta], (c + d + I e (2 k - m) + p)/d, -((b E^(d z))/a)])/ ((c + I e (2 k - m) - p) (c + I e (2 k - m) + p))), {k, 0, Floor[(1/2) (-1 + m)]}])/(1 + (b E^(d z))/a)^\[Beta] /; Element[m, Integers] && m > 0

 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