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/01.07.21.2386.01

 Input Form

 Integrate[1/(a + b Sin[e z] + c Cos[e z])^(3/2), z] == ((2 (a c + (b^2 + c^2) Cos[e z]))/b + (1/(b Sqrt[1 + c^2/b^2])) (2 a AppellF1[1/2, 1/2, 1/2, 3/2, (a + c Cos[e z] + b Sin[e z])/ (a + b Sqrt[1 + c^2/b^2]), (a + c Cos[e z] + b Sin[e z])/ (a - b Sqrt[1 + c^2/b^2])] Sec[e z + ArcTan[c/b]] Sqrt[((-c) Cos[e z] + b (Sqrt[1 + c^2/b^2] - Sin[e z]))/ (a + b Sqrt[1 + c^2/b^2])] (a + c Cos[e z] + b Sin[e z]) Sqrt[(c Cos[e z] + b (Sqrt[1 + c^2/b^2] + Sin[e z]))/ (-a + b Sqrt[1 + c^2/b^2])]) - (b ((b^2 + 2 c^2) Cos[e z] + c (2 a + b Sin[e z])))/(b^2 + c^2) - (b^2 AppellF1[-(1/2), -(1/2), -(1/2), 1/2, (a + c Cos[e z] + b Sin[e z])/ (a + Sqrt[1 + b^2/c^2] c), (a + c Cos[e z] + b Sin[e z])/ (a - Sqrt[1 + b^2/c^2] c)] Sin[e z - ArcTan[b/c]])/ (Sqrt[1 + b^2/c^2] c Sqrt[(Sqrt[1 + b^2/c^2] c - c Cos[e z] - b Sin[e z])/ (a + Sqrt[1 + b^2/c^2] c)] Sqrt[(Sqrt[1 + b^2/c^2] c + c Cos[e z] + b Sin[e z])/(-a + Sqrt[1 + b^2/c^2] c)]) - (c AppellF1[-(1/2), -(1/2), -(1/2), 1/2, (a + c Cos[e z] + b Sin[e z])/ (a + Sqrt[1 + b^2/c^2] c), (a + c Cos[e z] + b Sin[e z])/ (a - Sqrt[1 + b^2/c^2] c)] Sin[e z - ArcTan[b/c]])/ (Sqrt[1 + b^2/c^2] Sqrt[(Sqrt[1 + b^2/c^2] c - c Cos[e z] - b Sin[e z])/ (a + Sqrt[1 + b^2/c^2] c)] Sqrt[(Sqrt[1 + b^2/c^2] c + c Cos[e z] + b Sin[e z])/(-a + Sqrt[1 + b^2/c^2] c)]) - (c (2 a Sqrt[1 + b^2/c^2] c^2 + 2 c (b^2 + c^2) Cos[e z - ArcTan[b/c]] - b (b^2 + c^2) Sin[e z - ArcTan[b/c]]))/(b Sqrt[1 + b^2/c^2] (b^2 + c^2)))/((a^2 - b^2 - c^2) e Sqrt[a + c Cos[e z] + b Sin[e z]])

 Standard Form

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 MathML Form

 1 ( a + b sin ( e z ) + c cos ( e z ) ) 3 / 2 z ( - ( ( b 2 + 2 c 2 ) cos ( e z ) + c ( 2 a + b sin ( e z ) ) ) b b 2 + c 2 + 1 b c 2 b 2 + 1 ( 2 a F 1 AppellF1 ( 1 2 ; 1 2 , 1 2 ; 3 2 ; a + c cos ( e z ) + b sin ( e z ) a + b c 2 b 2 + 1 , a + c cos ( e z ) + b sin ( e z ) a - b c 2 b 2 + 1 ) sec ( e z + tan - 1 ( c b ) ) b ( c 2 b 2 + 1 - sin ( e z ) ) - c cos ( e z ) a + b c 2 b 2 + 1 ( a + c cos ( e z ) + b sin ( e z ) ) c cos ( e z ) + b ( sin ( e z ) + c 2 b 2 + 1 ) b c 2 b 2 + 1 - a ) - b 2 sin ( e z - tan - 1 ( b c ) ) b 2 c 2 + 1 c - cos ( e z ) c + b 2 c 2 + 1 c - b sin ( e z ) a + c b 2 c 2 + 1 cos ( e z ) c + b 2 c 2 + 1 c + b sin ( e z ) b 2 c 2 + 1 c - a F 1 AppellF1 ( - 1 2 ; - 1 2 , - 1 2 ; 1 2 ; a + c cos ( e z ) + b sin ( e z ) a + c b 2 c 2 + 1 , a + c cos ( e z ) + b sin ( e z ) a - b 2 c 2 + 1 c ) - c sin ( e z - tan - 1 ( b c ) ) b 2 c 2 + 1 - cos ( e z ) c + b 2 c 2 + 1 c - b sin ( e z ) a + c b 2 c 2 + 1 cos ( e z ) c + b 2 c 2 + 1 c + b sin ( e z ) b 2 c 2 + 1 c - a F 1 AppellF1 ( - 1 2 ; - 1 2 , - 1 2 ; 1 2 ; a + c cos ( e z ) + b sin ( e z ) a + c b 2 c 2 + 1 , a + c cos ( e z ) + b sin ( e z ) a - b 2 c 2 + 1 c ) - ( c ( 2 a b 2 c 2 + 1 c 2 + 2 ( b 2 + c 2 ) cos ( e z - tan - 1 ( b c ) ) c - b ( b 2 + c 2 ) sin ( e z - tan - 1 ( b c ) ) ) ) / ( b b 2 c 2 + 1 ( b 2 + c 2 ) ) + 2 ( a c + ( b 2 + c 2 ) cos ( e z ) ) b ) / ( ( a 2 - b 2 - c 2 ) e a + c cos ( e z ) + b sin ( e z ) ) z 1 a b e z c e z 3 2 -1 -1 b 2 2 c 2 e z c 2 a b e z b b 2 c 2 -1 1 b c 2 b 2 -1 1 1 2 -1 2 a AppellF1 1 2 1 2 1 2 3 2 a c e z b e z a b c 2 b 2 -1 1 1 2 -1 a c e z b e z a -1 b c 2 b 2 -1 1 1 2 -1 e z c b -1 b c 2 b 2 -1 1 1 2 -1 e z -1 c e z a b c 2 b 2 -1 1 1 2 -1 1 2 a c e z b e z c e z b e z c 2 b 2 -1 1 1 2 b c 2 b 2 -1 1 1 2 -1 a -1 1 2 -1 b 2 e z -1 b c -1 b 2 c 2 -1 1 1 2 c -1 e z c b 2 c 2 -1 1 1 2 c -1 b e z a c b 2 c 2 -1 1 1 2 -1 1 2 e z c b 2 c 2 -1 1 1 2 c b e z b 2 c 2 -1 1 1 2 c -1 a -1 1 2 -1 AppellF1 -1 1 2 -1 1 2 -1 1 2 1 2 a c e z b e z a c b 2 c 2 -1 1 1 2 -1 a c e z b e z a -1 b 2 c 2 -1 1 1 2 c -1 -1 c e z -1 b c -1 b 2 c 2 -1 1 1 2 -1 e z c b 2 c 2 -1 1 1 2 c -1 b e z a c b 2 c 2 -1 1 1 2 -1 1 2 e z c b 2 c 2 -1 1 1 2 c b e z b 2 c 2 -1 1 1 2 c -1 a -1 1 2 -1 AppellF1 -1 1 2 -1 1 2 -1 1 2 1 2 a c e z b e z a c b 2 c 2 -1 1 1 2 -1 a c e z b e z a -1 b 2 c 2 -1 1 1 2 c -1 -1 c 2 a b 2 c 2 -1 1 1 2 c 2 2 b 2 c 2 e z -1 b c -1 c -1 b b 2 c 2 e z -1 b c -1 b b 2 c 2 -1 1 1 2 b 2 c 2 -1 2 a c b 2 c 2 e z b -1 a 2 -1 b 2 -1 c 2 e a c e z b e z 1 2 -1 [/itex]

 Rule Form

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

 2002-12-18