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/01.07.21.2392.01

 Input Form

 Integrate[(a Sin[e z]^2 + b Cos[e z]^2)^(5/2), z] == (1/e) ((1/(60 Sqrt[2])) ((a - b) (-11 (a + b) + 3 (a - b) Cos[2 e z]) Sqrt[a + b + (-a + b) Cos[2 e z]] Sin[2 e z])) + (1/(15 Sqrt[2] e)) (-(4 I (8 a^3 + 7 a^2 b + 7 a b^2 + 8 b^3) Sqrt[a + b + (-a + b) Cos[2 e z]] Sqrt[(a + b + (-a + b) Cos[2 e z])/ (1 + Cos[e z])^2] 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)] Sec[(e z)/2]^2 Sqrt[1 + (b Tan[(e z)/2]^2)/ (2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ (Sqrt[-((-2 a + 2 Sqrt[a] Sqrt[a - b] + b)/b)] ((a + b + (-a + b) Cos[2 e z]) Sec[(e z)/2]^4)^(3/2)) + (Sqrt[2] (-8 a^3 + a^2 b - a b^2 + 8 b^3) (1 + Cos[e z]) Sqrt[(a + b - a Cos[2 e z] + b Cos[2 e z])/(1 + Cos[e z])^2] (((-(1/2)) (a + b + (-a + b) Cos[2 e z]) Sec[(e z)/2]^2 Tan[(e z)/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)] - 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[1 + (b Tan[(e z)/2]^2)/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] - (I a 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[1 + (b Tan[(e z)/2]^2)/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)] Sqrt[1 - (b Tan[(e z)/2]^2)/(-2 a + 2 Sqrt[a] Sqrt[a - b] + b)])/ Sqrt[b/(2 a + 2 Sqrt[a] Sqrt[a - b] - b)])/ ((a - b) Sqrt[4 a Tan[(e z)/2]^2 + b (-1 + Tan[(e z)/2]^2)^2])))/ Sqrt[a + b + (-a + b) Cos[2 e z]])

 Standard Form

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 MathML Form

 ( b cos 2 ( e z ) + a sin 2 ( e z ) ) 5 / 2 z 1 15 2 e ( ( 2 ( - 8 a 3 + b a 2 - b 2 a + 8 b 3 ) ( cos ( e z ) + 1 ) - cos ( 2 e z ) a + a + b + b cos ( 2 e z ) ( cos ( e z ) + 1 ) 2 ( - 1 2 ( a + b + ( b - a ) cos ( 2 e z ) ) tan ( e z 2 ) sec 2 ( e z 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 ) - 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 ) ) b tan 2 ( e z 2 ) 2 a + 2 a - b a - b + 1 1 - b tan 2 ( e z 2 ) - 2 a + 2 a - b a + b ) / ( b 2 a + 2 a - b a - b ) - ( a 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 ) b tan 2 ( e z 2 ) 2 a + 2 a - b a - b + 1 1 - b tan 2 ( e z 2 ) - 2 a + 2 a - b a + b ) / ( b 2 a + 2 a - b a - b ) ) ) / ( ( ( a - b ) 4 a tan 2 ( e z 2 ) + b ( tan 2 ( e z 2 ) - 1 ) 2 ) a + b + ( b - a ) cos ( 2 e z ) ) - ( 4 ( 8 a 3 + 7 b a 2 + 7 b 2 a + 8 b 3 ) a + b + ( b - a ) cos ( 2 e z ) a + b + ( b - a ) cos ( 2 e z ) ( cos ( e z ) + 1 ) 2 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 ) sec 2 ( e z 2 ) b tan 2 ( e z 2 ) 2 a + 2 a - b a - b + 1 1 - b tan 2 ( e z 2 ) - 2 a + 2 a - b a + b ) / ( - - 2 a + 2 a - b a + b b ( ( a + b + ( b - a ) cos ( 2 e z ) ) sec 4 ( e z 2 ) ) 3 / 2 ) ) + 1 e ( 60 2 ) ( ( a - b ) ( 3 ( a - b ) cos ( 2 e z ) - 11 ( a + b ) ) a + b + ( b - a ) cos ( 2 e z ) sin ( 2 e z ) ) z b e z 2 a e z 2 5 2 1 15 2 1 2 e -1 2 1 2 -8 a 3 b a 2 -1 b 2 a 8 b 3 e z 1 -1 2 e z a a b b 2 e z e z 1 2 -1 1 2 -1 1 2 a b b -1 a 2 e z e z 2 -1 e z 2 -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 -1 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 b e z 2 -1 2 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 1 2 1 -1 b e z 2 -1 2 -2 a 2 a -1 b 1 2 a 1 2 b -1 1 2 b 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 2 -1 -1 a 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 b e z 2 -1 2 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 1 2 1 -1 b e z 2 -1 2 -2 a 2 a -1 b 1 2 a 1 2 b -1 1 2 b 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 2 -1 a -1 b 4 a e z 2 -1 2 b e z 2 -1 2 -1 2 1 2 a b b -1 a 2 e z 1 2 -1 -1 4 8 a 3 7 b a 2 7 b 2 a 8 b 3 a b b -1 a 2 e z 1 2 a b b -1 a 2 e z e z 1 2 -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 e z 2 -1 2 b e z 2 -1 2 2 a 2 a -1 b 1 2 a 1 2 -1 b -1 1 1 2 1 -1 b e z 2 -1 2 -2 a 2 a -1 b 1 2 a 1 2 b -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 4 3 2 -1 1 e 60 2 1 2 -1 a -1 b 3 a -1 b 2 e z -1 11 a b a b b -1 a 2 e z 1 2 2 e z [/itex]

 Rule Form

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

 2002-12-18