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/01.20.21.4405.01

 Input Form

 Integrate[(a + b Sinh[e z] + c Cosh[e z])^\[Beta] (A + B Sinh[e z] + C Cosh[e z]), z] == (b B AppellF1[\[Beta], -(1/2), -(1/2), 1 + \[Beta], (a + c Cosh[e z] + b Sinh[e z])/(a + Sqrt[1 - b^2/c^2] c), (a + c Cosh[e z] + b Sinh[e z])/(a - Sqrt[1 - b^2/c^2] c)] (a + c Cosh[e z] + b Sinh[e z])^\[Beta] Sinh[e z + ArcTanh[b/c]])/ (Sqrt[1 - b^2/c^2] c e Sqrt[(Sqrt[1 - b^2/c^2] c (1 + Cosh[e z + ArcTanh[b/c]]))/ (-a + Sqrt[1 - b^2/c^2] c)] Sqrt[(Sqrt[1 - b^2/c^2] c - c Cosh[e z] - b Sinh[e z])/ (a + Sqrt[1 - b^2/c^2] c)]) - (1/e) (B (a + c Cosh[e z] + b Sinh[e z])^\[Beta] (-((c (a + c Cosh[e z] + b Sinh[e z]))/((-b^2 + c^2) (1 + \[Beta]))) + (b Sinh[e z + ArcTanh[b/c]])/(Sqrt[1 - b^2/c^2] c))) + (A AppellF1[1 + \[Beta], 1/2, 1/2, 2 + \[Beta], (a + c Cosh[e z] + b Sinh[e z])/(a + I b Sqrt[1 - c^2/b^2]), (a + c Cosh[e z] + b Sinh[e z])/(a - I b Sqrt[1 - c^2/b^2])] Sech[e z + ArcTanh[c/b]] (a + c Cosh[e z] + b Sinh[e z])^(1 + \[Beta]) Sqrt[-((c Cosh[e z] + b ((-I) Sqrt[1 - c^2/b^2] + Sinh[e z]))/ (a + I b Sqrt[1 - c^2/b^2]))] Sqrt[-((b Sqrt[1 - c^2/b^2] (I + Sinh[e z + ArcTanh[c/b]]))/ (a - I b Sqrt[1 - c^2/b^2]))])/(b Sqrt[1 - c^2/b^2] e (1 + \[Beta])) - (1/(b e)) (C (a + c Cosh[e z] + b Sinh[e z])^\[Beta] ((c Cosh[e z + ArcTanh[c/b]])/Sqrt[1 - c^2/b^2] - (b^2 (a + c Cosh[e z] + b Sinh[e z]))/((b^2 - c^2) (1 + \[Beta])) - (c AppellF1[\[Beta], -(1/2), -(1/2), 1 + \[Beta], (a + c Cosh[e z] + b Sinh[e z])/(a + I b Sqrt[1 - c^2/b^2]), (a + c Cosh[e z] + b Sinh[e z])/(a - I b Sqrt[1 - c^2/b^2])] Cosh[e z + ArcTanh[c/b]])/(Sqrt[1 - c^2/b^2] Sqrt[-((c Cosh[e z] + b ((-I) Sqrt[1 - c^2/b^2] + Sinh[e z]))/ (a + I b Sqrt[1 - c^2/b^2]))] Sqrt[-((b Sqrt[1 - c^2/b^2] (I + Sinh[e z + ArcTanh[c/b]]))/ (a - I b Sqrt[1 - c^2/b^2]))])))

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18