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Cos




Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving algebraic functions of sin > Involving sin(e z)cos(c z)(a+b sin(d z))beta





http://functions.wolfram.com/01.07.21.0748.01









  


  








Input Form





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








Standard Form





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MathML Form







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





2002-12-18