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Sin




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.06.21.1438.01









  


  








Input Form





Integrate[(E^(p z) Sin[c z])/(a + b Sin[c z]^2), z] == (I/(2 Sqrt[a] b Sqrt[a + b])) ((1/((-I) c + p)) (E^(((-I) c + p) z) ((2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[(c + I p)/(2 c), 1, 3/2 + (I p)/(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[(c + I p)/(2 c), 1, 3/2 + (I p)/(2 c), b/(E^(2 I c z) (2 a + b + 2 Sqrt[a] Sqrt[a + b]))])) - (1/(-3 I c + p)) (E^((-3 I c + p) z) ((2 a + b + 2 Sqrt[a] Sqrt[a + b]) Hypergeometric2F1[3/2 + (I p)/(2 c), 1, 5/2 + (I p)/(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[3/2 + (I p)/(2 c), 1, 5/2 + (I p)/(2 c), b/(E^(2 I c z) (2 a + b + 2 Sqrt[a] Sqrt[a + b]))])))








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