html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Cosh

 http://functions.wolfram.com/01.20.21.4243.01

 Input Form

 Integrate[Cosh[z]^2/(Sqrt[a + b Sinh[z]] (c + b Sinh[z])^2), z] == (1/(4 b (a - c))) (-((1/(Sqrt[1/(-a + I b)] b^2 (a - c))) (8 I a ((a - c) EllipticF[I ArcSinh[Sqrt[1/(-a + I b)] Sqrt[a + b Sinh[z]]], (a - I b)/(a + I b)] + c EllipticPi[(a - I b)/(a - c), I ArcSinh[Sqrt[1/(-a + I b)] Sqrt[a + b Sinh[z]]], (a - I b)/(a + I b)]) Sech[z] Sqrt[(b - I b Sinh[z])/(I a + b)] Sqrt[(b + I b Sinh[z])/ ((-I) a + b)])) + (1/(Sqrt[1/(-a + I b)] b^2 (a - c))) (I (Cosh[z] + Cosh[3 z]) (2 (a + I b) (a - c) EllipticE[I ArcSinh[Sqrt[1/(-a + I b)] Sqrt[a + b Sinh[z]]], (a - I b)/(a + I b)] + 2 (a - c) ((-I) b + c) EllipticF[I ArcSinh[Sqrt[1/(-a + I b)] Sqrt[a + b Sinh[z]]], (a - I b)/(a + I b)] + (b^2 + 2 c^2) EllipticPi[(a - I b)/(a - c), I ArcSinh[Sqrt[1/(-a + I b)] Sqrt[a + b Sinh[z]]], (a - I b)/(a + I b)]) Sech[z]^2 Sech[2 z] Sqrt[(b - I b Sinh[z])/(I a + b)] Sqrt[(b + I b Sinh[z])/((-I) a + b)]) + (6 b EllipticPi[(2 b)/(b + I c), (1/4) (Pi - 2 I z), -((2 I b)/(a - I b))] Sqrt[(a + b Sinh[z])/(a - I b)])/((b + I c) Sqrt[a + b Sinh[z]]) - (4 Cosh[z] Sqrt[a + b Sinh[z]])/(c + b Sinh[z]))

 Standard Form

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 MathML Form

 cosh 2 ( z ) a + b sinh ( z ) ( c + b sinh ( z ) ) 2 z 1 4 b ( a - c ) ( 1 1 b - a b 2 ( a - c ) ( ( cosh ( z ) + cosh ( 3 z ) ) ( 2 ( a + b ) ( a - c ) E ( sinh - 1 ( 1 b - a a + b sinh ( z ) ) a - b a + b ) + 2 ( a - c ) ( c - b ) F ( sinh - 1 ( 1 b - a a + b sinh ( z ) ) a - b a + b ) + ( b 2 + 2 c 2 ) Π ( a - b a - c ; sinh - 1 ( 1 b - a a + b sinh ( z ) ) a - b a + b ) ) sech ( 2 z ) b - b sinh ( z ) a + b sinh ( z ) b + b b - a sech 2 ( z ) ) - 1 1 b - a b 2 ( a - c ) ( 8 a ( ( a - c ) F ( sinh - 1 ( 1 b - a a + b sinh ( z ) ) a - b a + b ) + c Π ( a - b a - c ; sinh - 1 ( 1 b - a a + b sinh ( z ) ) a - b a + b ) ) b - b sinh ( z ) a + b sinh ( z ) b + b b - a sech ( z ) ) + 6 b Π ( 2 b b + c ; 1 4 ( π - 2 z ) - 2 b a - b ) a + b sinh ( z ) a - b ( b + c ) a + b sinh ( z ) - 4 cosh ( z ) a + b sinh ( z ) c + b sinh ( z ) ) z z 2 a b z 1 2 c b z 2 -1 1 4 b a -1 c -1 1 1 b -1 a -1 1 2 b 2 a -1 c -1 z 3 z 2 a b a -1 c EllipticE 1 b -1 a -1 1 2 a b z 1 2 a -1 b a b -1 2 a -1 c c -1 b EllipticF 1 b -1 a -1 1 2 a b z 1 2 a -1 b a b -1 b 2 2 c 2 EllipticPi a -1 b a -1 c -1 1 b -1 a -1 1 2 a b z 1 2 a -1 b a b -1 2 z b -1 b z a b -1 1 2 z b b b -1 a -1 1 2 z 2 -1 1 1 b -1 a -1 1 2 b 2 a -1 c -1 8 a a -1 c EllipticF 1 b -1 a -1 1 2 a b z 1 2 a -1 b a b -1 c EllipticPi a -1 b a -1 c -1 1 b -1 a -1 1 2 a b z 1 2 a -1 b a b -1 b -1 b z a b -1 1 2 z b b b -1 a -1 1 2 z 6 b EllipticPi 2 b b c -1 1 4 -1 2 z -1 2 b a -1 b -1 a b z a -1 b -1 1 2 b c a b z 1 2 -1 -1 4 z a b z 1 2 c b z -1 [/itex]

 Rule Form

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

 2002-12-18