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/01.07.21.2397.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2002-12-18