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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving algebraic functions of the direct function, trigonometric and exponential functions > Involving sin and exp > Involving ep zsin(d z)(a+b cos2(c z))beta





http://functions.wolfram.com/01.07.21.2693.01









  


  










Input Form





Integrate[E^(p z) Sin[d z] (a + b Cos[c z]^2)^\[Beta], z] == (I (a + ((1/4) b (1 + E^(2 I c z))^2)/E^(2 I c z))^\[Beta] (I E^((I d + p) z) (d + I p + 2 c \[Beta]) AppellF1[(d - I p - 2 c \[Beta])/(2 c), -\[Beta], -\[Beta], (2 c + d - I p - 2 c \[Beta])/(2 c), -((b E^(2 I c z))/(2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 I c z))/(2 a + b - 2 Sqrt[a (a + b)]))] + E^(((-I) d + p) z) (I d + p - 2 I c \[Beta]) AppellF1[-((d + I p + 2 c \[Beta])/(2 c)), -\[Beta], -\[Beta], -((d + I p + 2 c (-1 + \[Beta]))/(2 c)), -((b E^(2 I c z))/(2 a + b + 2 Sqrt[a (a + b)])), -((b E^(2 I c z))/(2 a + b - 2 Sqrt[a (a + b)]))]))/ ((1 + (b E^(2 I c z))/(2 a + b - 2 Sqrt[a (a + b)]))^\[Beta] (1 + (b E^(2 I c z))/(2 a + b + 2 Sqrt[a (a + b)]))^\[Beta])/ (2 (d^2 + (p - 2 I c \[Beta])^2))










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