Integrate[E^(p z) Sinh[e z] Cosh[c z] (a + b Sinh[d z])^\[Beta], z] == ((1/4) (-((1/(c - e + p + d \[Beta])) (E^((c - e + p) z) AppellF1[-((c - e + p)/d) - \[Beta], -\[Beta], -\[Beta], 1 - (c - e + p)/d - \[Beta], b/(E^(d z) (a + Sqrt[a^2 + b^2])), b/(E^(d z) (a - Sqrt[a^2 + b^2]))])) + (1/(-c + e + p + d \[Beta])) (E^((-c + e + p) z) AppellF1[-((-c + e + p)/d) - \[Beta], -\[Beta], -\[Beta], 1 - (-c + e + p)/d - \[Beta], b/(E^(d z) (a + Sqrt[a^2 + b^2])), b/(E^(d z) (a - Sqrt[a^2 + b^2]))]) + (1/(c + e + p + d \[Beta])) (E^((c + e + p) z) AppellF1[-((c + e + p)/d) - \[Beta], -\[Beta], -\[Beta], 1 - (c + e + p)/d - \[Beta], b/(E^(d z) (a + Sqrt[a^2 + b^2])), b/(E^(d z) (a - Sqrt[a^2 + b^2]))]) + (1/(c + e - p - d \[Beta])) (E^((-c - e + p) z) AppellF1[(c + e - p - d \[Beta])/d, -\[Beta], -\[Beta], -((I (I d + I (c + e - p) - I d \[Beta]))/d), b/(E^(d z) (a + Sqrt[a^2 + b^2])), b/(E^(d z) (a - Sqrt[a^2 + b^2]))])) (a + b Sinh[d z])^\[Beta])/ ((1 + b/(E^(d z) (-a + Sqrt[a^2 + b^2])))^\[Beta] (1 - b/(E^(d z) (a + Sqrt[a^2 + b^2])))^\[Beta])

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2002-12-18