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; }

 Tan

 http://functions.wolfram.com/01.08.21.0213.01

 Input Form

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

 Standard Form

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FractionBox[RowBox[List["c", " ", "z"]], "2"], "]"]], "4"]]]], " ", SqrtBox[RowBox[List["a", "+", RowBox[List["b", " ", SuperscriptBox[RowBox[List["Tan", "[", RowBox[List["c", " ", "z"]], "]"]], "2"]]]]]]]], ")"]]]]]]]]

 MathML Form

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

 Rule Form

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

 2002-12-18

© 1998-2013 Wolfram Research, Inc.