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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving rational functions of the direct function > Involving sin(d z)/a+b sin2(c z)





http://functions.wolfram.com/01.06.21.0860.01









  


  










Input Form





Integrate[Sin[d z]/(a + b Sin[c z]^2), z] == (-(1/(2 Sqrt[a] b Sqrt[a + b]))) ((1/(2 c - d)) (E^(-2 I c z + I d z) ((2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - d/(2 c), 1, 2 - d/(2 c), b/(E^(2 I c z) (2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 - d/(2 c), 1, 2 - d/(2 c), b/(E^(2 I c z) (2 a + b + 2 Sqrt[a] Sqrt[a + b]))])) - (1/(2 c + d)) (((2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[ 1 + d/(2 c), 1, 2 + d/(2 c), b/(E^(2 I c z) (2 a + b - 2 Sqrt[a] Sqrt[a + b]))] + (-2 a - b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[1 + d/(2 c), 1, 2 + d/(2 c), b/(E^(2 I c z) (2 a + b + 2 Sqrt[a] Sqrt[a + b]))])/ E^(I (2 c + d) z)))










Standard Form





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MathML Form







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Rule Form





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





2002-12-18