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 Tanh

 http://functions.wolfram.com/01.21.21.0361.01

 Input Form

 Integrate[Cosh[c z] Sqrt[a + b Tanh[c z]], z] == (1/(2 c)) (Sech[c z] ((2 b)/Sqrt[a + b Tanh[c z]] + Sinh[2 c z] Sqrt[a + b Tanh[c z]] + (2 I a^2 Cosh[c z] (EllipticE[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)] - EllipticF[ I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)]) (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])])/(Sqrt[-a - b] (a - b) b) + (1/(Sqrt[-a - b] b)) (2 I a Cosh[c z] EllipticF[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], (a - b)/(a + b)] (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])]) - (2 I b Cosh[c z] (EllipticE[I ArcSinh[Sqrt[-a - b]/ Sqrt[a + b Tanh[c z]]], -1 + (2 a)/(a + b)] - EllipticF[I ArcSinh[Sqrt[-a - b]/Sqrt[a + b Tanh[c z]]], -1 + (2 a)/(a + b)]) (a Cosh[c z] + b Sinh[c z]) Sqrt[(b (1 + Tanh[c z]))/(a + b Tanh[c z])] Sqrt[1 - (a + b)/(a + b Tanh[c z])])/(Sqrt[-a - b] (a - b))))

 Standard Form

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")"]]]]]]]]

 MathML Form

 cosh ( c z ) a + b tanh ( c z ) z 1 2 c ( sech ( c z ) ( 1 - a - b ( a - b ) b ( 2 a 2 cosh ( c z ) ( E ( sinh - 1 ( - a - b a + b tanh ( c z ) ) a - b a + b ) - F ( sinh - 1 ( - a - b a + b tanh ( c z ) ) a - b a + b ) ) ( a cosh ( c z ) + b sinh ( c z ) ) b ( tanh ( c z ) + 1 ) a + b tanh ( c z ) 1 - a + b a + b tanh ( c z ) ) + 1 - a - b b ( 2 a cosh ( c z ) F ( sinh - 1 ( - a - b a + b tanh ( c z ) ) a - b a + b ) ( a cosh ( c z ) + b sinh ( c z ) ) b ( tanh ( c z ) + 1 ) a + b tanh ( c z ) 1 - a + b a + b tanh ( c z ) ) + sinh ( 2 c z ) a + b tanh ( c z ) - 1 - a - b ( a - b ) ( 2 b cosh ( c z ) ( E ( sinh - 1 ( - a - b a + b tanh ( c z ) ) 2 a a + b - 1 ) - F ( sinh - 1 ( - a - b a + b tanh ( c z ) ) 2 a a + b - 1 ) ) ( a cosh ( c z ) + b sinh ( c z ) ) b ( tanh ( c z ) + 1 ) a + b tanh ( c z ) 1 - a + b a + b tanh ( c z ) ) + 2 b a + b tanh ( c z ) ) ) z c z a b c z 1 2 1 2 c -1 c z 1 -1 a -1 b 1 2 a -1 b b -1 2 a 2 c z EllipticE -1 a -1 b 1 2 a b c z 1 2 -1 a -1 b a b -1 -1 EllipticF -1 a -1 b 1 2 a b c z 1 2 -1 a -1 b a b -1 a c z b c z b c z 1 a b c z -1 1 2 1 -1 a b a b c z -1 1 2 1 -1 a -1 b 1 2 b -1 2 a c z EllipticF -1 a -1 b 1 2 a b c z 1 2 -1 a -1 b a b -1 a c z b c z b c z 1 a b c z -1 1 2 1 -1 a b a b c z -1 1 2 2 c z a b c z 1 2 -1 1 -1 a -1 b 1 2 a -1 b -1 2 b c z EllipticE -1 a -1 b 1 2 a b c z 1 2 -1 2 a a b -1 -1 -1 EllipticF -1 a -1 b 1 2 a b c z 1 2 -1 2 a a b -1 -1 a c z b c z b c z 1 a b c z -1 1 2 1 -1 a b a b c z -1 1 2 2 b a b c z 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18