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/01.20.21.4440.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18