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; }

 Cos

 http://functions.wolfram.com/01.07.21.2394.01

 Input Form

 Integrate[Sqrt[a Sin[e z]^2 + b Cos[e z]^2], z] == ((1 + Cos[e z]) Sqrt[(a + b + (-a + b) Cos[2 e z])/(1 + Cos[e z])^2] (Sqrt[-((-2 a + 2 Sqrt[a] Sqrt[a - b] + b)/b)] (a + b + (-a + b) Cos[2 e z]) Sec[(e z)/2]^2 Tan[(e z)/2] - 2 I (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) EllipticE[I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[(e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] Sqrt[(b + (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Tan[(e z)/2]^2)/b] Sqrt[(b - (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Tan[(e z)/2]^2)/b] + 4 I Sqrt[a] (-Sqrt[a] + Sqrt[a - b]) EllipticF[I ArcSinh[Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Tan[(e z)/2]], (-2 a - 2 Sqrt[a] Sqrt[a - b] + b)/ (-2 a + 2 Sqrt[a] Sqrt[a - b] + b)] Sqrt[(b + (2 a + 2 Sqrt[a] Sqrt[a - b] - b) Tan[(e z)/2]^2)/b] Sqrt[(b - (-2 a + 2 Sqrt[a] Sqrt[a - b] + b) Tan[(e z)/2]^2)/b]))/ (2 Sqrt[-((-2 a + 2 Sqrt[a] Sqrt[a - b] + b)/b)] e Sqrt[a + b + (-a + b) Cos[2 e z]] Sqrt[4 a Tan[(e z)/2]^2 + b (-1 + Tan[(e z)/2]^2)^2])

 Standard Form

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 MathML Form

 a sin 2 ( e z ) + b cos 2 ( e z ) z ( ( cos ( e z ) + 1 ) a + b + ( b - a ) cos ( 2 e z ) ( cos ( e z ) + 1 ) 2 ( - - 2 a + 2 a - b a + b b ( a + b + ( b - a ) cos ( 2 e z ) ) tan ( e z 2 ) sec 2 ( e z 2 ) + 4 a ( a - b - a ) ( 2 a + 2 a - b a - b ) tan 2 ( e z 2 ) + b b b - ( - 2 a + 2 a - b a + b ) tan 2 ( e z 2 ) b F ( sinh - 1 ( b 2 a + 2 a - b a - b tan ( e z 2 ) ) - 2 a - 2 a - b a + b - 2 a + 2 a - b a + b ) - 2 ( - 2 a + 2 a - b a + b ) E ( sinh - 1 ( b 2 a + 2 a - b a - b tan ( e z 2 ) ) - 2 a - 2 a - b a + b - 2 a + 2 a - b a + b ) ( 2 a + 2 a - b a - b ) tan 2 ( e z 2 ) + b b b - ( - 2 a + 2 a - b a + b ) tan 2 ( e z 2 ) b ) ) / ( 2 - - 2 a + 2 a - b a + b b e a + b + ( b - a ) cos ( 2 e z ) 4 a tan 2 ( e z 2 ) + b ( tan 2 ( e z 2 ) - 1 ) 2 ) z a e z 2 b e z 2 1 2 e z 1 a b b -1 a 2 e z e z 1 2 -1 1 2 -1 -2 a 2 a -1 b 1 2 a 1 2 b b -1 1 2 a b b -1 a 2 e z e z 2 -1 e z 2 -1 2 4 a 1 2 a -1 b 1 2 -1 a 1 2 2 a 2 a -1 b 1 2 a 1 2 -1 b e z 2 -1 2 b b -1 1 2 b -1 -2 a 2 a -1 b 1 2 a 1 2 b e z 2 -1 2 b -1 1 2 EllipticF b 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 2 e z 2 -1 -2 a -1 2 a -1 b 1 2 a 1 2 b -2 a 2 a -1 b 1 2 a 1 2 b -1 -1 2 -2 a 2 a -1 b 1 2 a 1 2 b EllipticE b 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 2 e z 2 -1 -2 a -1 2 a -1 b 1 2 a 1 2 b -2 a 2 a -1 b 1 2 a 1 2 b -1 2 a 2 a -1 b 1 2 a 1 2 -1 b e z 2 -1 2 b b -1 1 2 b -1 -2 a 2 a -1 b 1 2 a 1 2 b e z 2 -1 2 b -1 1 2 2 -1 -2 a 2 a -1 b 1 2 a 1 2 b b -1 1 2 e a b b -1 a 2 e z 1 2 4 a e z 2 -1 2 b e z 2 -1 2 -1 2 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18