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 Csch

 http://functions.wolfram.com/01.23.21.0130.01

 Input Form

 Integrate[(a + b Cosh[2 c z])^\[Beta] Csch[c z], z] == (1/(4 c \[Beta])) ((AppellF1[-2 \[Beta], -\[Beta], -\[Beta], 1 - 2 \[Beta], -((2 + Sqrt[2 - (2 a)/b])/(2 (-1 + Cosh[c z]))), (-2 + Sqrt[2 - (2 a)/b])/(-2 + 2 Cosh[c z])]/ (((Sqrt[2 - (2 a)/b] + 2 Cosh[c z])/(-1 + Cosh[c z]))^\[Beta] ((-Sqrt[2 - (2 a)/b] + 2 Cosh[c z])/(-4 + 4 Cosh[c z]))^\[Beta]) - AppellF1[-2 \[Beta], -\[Beta], -\[Beta], 1 - 2 \[Beta], -((-2 + Sqrt[2 - (2 a)/b])/(2 (1 + Cosh[c z]))), (2 + Sqrt[2 - (2 a)/b])/(2 + 2 Cosh[c z])]/ (((Sqrt[2 - (2 a)/b] + 2 Cosh[c z])/(1 + Cosh[c z]))^\[Beta] ((-Sqrt[2 - (2 a)/b] + 2 Cosh[c z])/(4 + 4 Cosh[c z]))^\[Beta])) (a + b Cosh[2 c z])^\[Beta])

 Standard Form

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 MathML Form

 ( a + b cosh ( 2 c z ) ) β csch ( c z ) z 1 4 c β ( ( F 1 AppellF1 ( - 2 β ; - β , - β ; 1 - 2 β ; - 2 - 2 a b + 2 2 ( cosh ( c z ) - 1 ) , 2 - 2 a b - 2 2 cosh ( c z ) - 2 ) ( 2 cosh ( c z ) + 2 - 2 a b cosh ( c z ) - 1 ) - β ( 2 cosh ( c z ) - 2 - 2 a b 4 cosh ( c z ) - 4 ) - β - F 1 AppellF1 ( - 2 β ; - β , - β ; 1 - 2 β ; - 2 - 2 a b - 2 2 ( cosh ( c z ) + 1 ) , 2 - 2 a b + 2 2 cosh ( c z ) + 2 ) ( 2 cosh ( c z ) + 2 - 2 a b cosh ( c z ) + 1 ) - β ( 2 cosh ( c z ) - 2 - 2 a b 4 cosh ( c z ) + 4 ) - β ) ( a + b cosh ( 2 c z ) ) β ) z a b 2 c z β c z 1 4 c β -1 AppellF1 -2 β -1 β -1 β 1 -1 2 β -1 2 -1 2 a b -1 1 2 2 2 c z -1 -1 2 -1 2 a b -1 1 2 -2 2 c z -2 -1 2 c z 2 -1 2 a b -1 1 2 c z -1 -1 -1 β 2 c z -1 2 -1 2 a b -1 1 2 4 c z -4 -1 -1 β -1 AppellF1 -2 β -1 β -1 β 1 -1 2 β -1 2 -1 2 a b -1 1 2 -2 2 c z 1 -1 2 -1 2 a b -1 1 2 2 2 c z 2 -1 2 c z 2 -1 2 a b -1 1 2 c z 1 -1 -1 β 2 c z -1 2 -1 2 a b -1 1 2 4 c z 4 -1 -1 β a b 2 c z β [/itex]

 Rule Form

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

 2002-12-18